All Electronics & Telecommunication MCQs

Browse Electronics & Telecommunication Engineering MCQs with four options, hidden answers, concise explanations and references where available. Questions are organized in pages of up to 100 for focused practice.

Question 1701

Network TheoryNetwork Functions

A unit-step input has Laplace transform 1/s. For H(s)=5/(s+5), the output transform is?

A5/(s+5)
B1/[s(s+5)]
C5/[s(s+5)]
Ds/(s+5)

Show AnswerHide Answer Report an error

Correct Answer: C. 5/[s(s+5)]

Explanation: Y(s)=H(s)X(s)=[5/(s+5)](1/s)=5/[s(s+5)].

Reference: Standard network theory: step response in s-domain

Question 1702

Network TheoryNetwork Functions

For H(s)=5/(s+5) excited by a unit step, the final output value is?

Show AnswerHide Answer Report an error

Correct Answer: B. 1

Explanation: Using the final-value theorem, y(infinity)=lim(s->0) s·5/[s(s+5)]=5/5=1.

Reference: Standard network theory: step final value

Question 1703

Network TheoryNetwork Functions

The convolution integral for the zero-state output of a continuous-time LTI network is?

Ay(t)=integral x(tau)h(t-tau)d tau
By(t)=x(t)+h(t)
Cy(t)=x(t)/h(t)
Dy(t)=dx(t)/dt only

Show AnswerHide Answer Report an error

Correct Answer: A. y(t)=integral x(tau)h(t-tau)d tau

Explanation: The zero-state response of an LTI system is the convolution of the input x(t) with the impulse response h(t).

Reference: Standard network theory: convolution

Question 1704

Network TheoryNetwork Functions

If x(t)=delta(t) is applied to an LTI network with impulse response h(t), the zero-state output is?

A0
B1
Ch(t)
DIntegral of h(t) only

Show AnswerHide Answer Report an error

Correct Answer: C. h(t)

Explanation: The delta function is the identity element of convolution: delta(t)*h(t)=h(t).

Reference: Standard network theory: impulse input

Question 1705

Network TheoryNetwork Functions

For two causal LTI networks with transfer functions H1(s)=1/(s+1) and H2(s)=2/(s+3) connected in cascade, the overall transfer function is?

A3/(2s+4)
B2/[(s+1)(s+3)]
C2/(s+4)
D1/[(s+1)+(s+3)]

Show AnswerHide Answer Report an error

Correct Answer: B. 2/[(s+1)(s+3)]

Explanation: Transfer functions multiply in cascade, so H(s)=H1(s)H2(s)=2/[(s+1)(s+3)].

Reference: Standard network theory: cascade transfer functions

Question 1706

Network TheoryNetwork Topology

In a connected planar graph with n nodes and b branches, the number of independent meshes is?

An-1
Bb-n+1
Cb+n-1
Db-1

Show AnswerHide Answer Report an error

Correct Answer: B. b-n+1

Explanation: For a connected planar network, the number of independent meshes is b-n+1.

Reference: Standard network theory: planar graph topology

Question 1707

Network TheoryNetwork Topology

A connected network graph has 7 nodes and 11 branches. How many independent cut-set equations can be formed from a tree?

Show AnswerHide Answer Report an error

Correct Answer: B. 6

Explanation: A tree of a connected graph has n-1 twigs, and each twig defines one fundamental cut-set. Thus 7-1=6.

Reference: Standard network theory: fundamental cut-set count

Question 1708

Network TheoryNetwork Topology

For an oriented graph, each column of the node-branch incidence matrix corresponding to an ordinary branch contains?

AOne +1 and one -1
BTwo +1 entries only
COne nonzero entry only
DAll zero entries

Show AnswerHide Answer Report an error

Correct Answer: A. One +1 and one -1

Explanation: An oriented branch leaves one node and enters another, so its incidence-matrix column has one +1 and one -1 under a consistent sign convention.

Reference: Standard network theory: incidence matrix structure

Question 1709

Network TheoryNetwork Topology

If one row is deleted from the incidence matrix of a connected graph, the resulting reduced incidence matrix has how many rows for n nodes?

An
Bn-1
Cb-n+1
Db

Show AnswerHide Answer Report an error

Correct Answer: B. n-1

Explanation: Deleting the dependent reference-node row leaves a reduced incidence matrix with n-1 rows.

Reference: Standard network theory: reduced incidence matrix

Question 1710

Network TheoryNetwork Topology

A tie-set matrix is primarily used to express branch currents in terms of?

AIndependent loop currents
BNode voltages only
CBranch powers
DCut-set voltages only

Show AnswerHide Answer Report an error

Correct Answer: A. Independent loop currents

Explanation: Tie-set or fundamental-loop analysis relates branch currents to a set of independent loop currents.

Reference: Standard network theory: tie-set matrix

Question 1711

Network TheoryNetwork Topology

A cut-set matrix is particularly associated with writing independent forms of?

AKCL equations
BKVL equations only
CPower equations only
DTransformer equations

Show AnswerHide Answer Report an error

Correct Answer: A. KCL equations

Explanation: Cut-set equations express current conservation across cuts of a graph and therefore provide independent KCL relations.

Reference: Standard network theory: cut-set matrix

Question 1712

Network TheorySource Transformation

A network has a 12 V ideal voltage source in series with 3 ohm. Its equivalent Norton current is?

A2 A
B3 A
C4 A
D36 A

Show AnswerHide Answer Report an error

Correct Answer: C. 4 A

Explanation: Source transformation gives IN=V/R=12/3=4 A, with the same 3 ohm resistance in parallel.

Reference: Standard network theory: source transformation numerical

Question 1713

Network TheorySource Transformation

A Norton source of 5 A in parallel with 8 ohm is transformed to a Thevenin source of?

A5 V in series with 8 ohm
B13 V in series with 8 ohm
C40 V in series with 8 ohm
D40 V in series with 1.6 ohm

Show AnswerHide Answer Report an error

Correct Answer: C. 40 V in series with 8 ohm

Explanation: Vth=IN RN=5×8=40 V and Rth=RN=8 ohm.

Reference: Standard network theory: Norton to Thevenin numerical

Question 1714

Network TheoryNetwork Theorems

For a linear circuit containing several independent sources, superposition is applied to calculate?

AVoltages and currents, not power directly
BPower directly by adding individual source powers at an element
CEquivalent resistance only
DFrequency only

Show AnswerHide Answer Report an error

Correct Answer: A. Voltages and currents, not power directly

Explanation: Superposition applies to linear response quantities such as voltage and current. Power is nonlinear in voltage/current and cannot generally be superposed directly.

Reference: Standard network theory: superposition limitation

Question 1715

Network TheoryNetwork Theorems

While applying superposition, an independent ideal voltage source that is not being considered is replaced by?

AAn open circuit
BA short circuit
CIts internal power rating
DA dependent source

Show AnswerHide Answer Report an error

Correct Answer: B. A short circuit

Explanation: Setting an ideal independent voltage source to zero volts makes it a short circuit.

Reference: Standard network theory: superposition voltage-source suppression

Question 1716

Network TheoryNetwork Theorems

While applying superposition, an independent ideal current source that is not being considered is replaced by?

AA short circuit
BAn open circuit
CA voltage source of equal value
DA resistor of 1 ohm

Show AnswerHide Answer Report an error

Correct Answer: B. An open circuit

Explanation: Setting an ideal independent current source to zero amperes makes it an open circuit.

Reference: Standard network theory: superposition current-source suppression

Question 1717

Network TheoryCircuit Analysis

A 20 V source is connected to two series resistors of 4 ohm and 6 ohm. The voltage across the 6 ohm resistor is?

A8 V
B10 V
C12 V
D15 V

Show AnswerHide Answer Report an error

Correct Answer: C. 12 V

Explanation: By voltage division, V6=20×6/(4+6)=12 V.

Reference: Standard network theory: voltage divider numerical

Question 1718

Network TheoryCircuit Analysis

A total current of 10 A divides between parallel resistors 6 ohm and 3 ohm. The current through the 6 ohm branch is?

A2 A
B3.33 A
C5 A
D6.67 A

Show AnswerHide Answer Report an error

Correct Answer: B. 3.33 A

Explanation: For two parallel resistors, current through 6 ohm is 10×3/(6+3)=3.33 A.

Reference: Standard network theory: current divider numerical

Question 1719

Network TheoryCircuit Analysis

Three resistors 2 ohm, 3 ohm and 6 ohm are connected in parallel. Their equivalent resistance is?

A1 ohm
B2 ohm
C3 ohm
D11 ohm

Show AnswerHide Answer Report an error

Correct Answer: A. 1 ohm

Explanation: 1/Req=1/2+1/3+1/6=1, hence Req=1 ohm.

Reference: Standard network theory: parallel resistance numerical

Question 1720

Network TheoryCircuit Analysis

A 4 ohm resistor dissipates 36 W. The magnitude of current through it is?

A1.5 A
B3 A
C6 A
D9 A

Show AnswerHide Answer Report an error

Correct Answer: B. 3 A

Explanation: Using P=I^2R, I=sqrt(36/4)=3 A.

Reference: Standard network theory: resistor power numerical

Question 1721

Network TheoryAC Circuit Analysis

A sinusoidal voltage has RMS value 230 V. Its peak value is approximately?

A162.6 V
B230 V
C325.3 V
D460 V

Show AnswerHide Answer Report an error

Correct Answer: C. 325.3 V

Explanation: For a sinusoid, Vpeak=sqrt(2)Vrms≈1.414×230=325.3 V.

Reference: Standard network theory: RMS to peak numerical

Question 1722

Network TheoryAC Circuit Analysis

A sinusoidal current has peak value 10 A. Its RMS value is approximately?

A5 A
B7.07 A
C10 A
D14.14 A

Show AnswerHide Answer Report an error

Correct Answer: B. 7.07 A

Explanation: For a sine wave, Irms=Ipeak/sqrt(2)=10/1.414≈7.07 A.

Reference: Standard network theory: peak to RMS numerical

Question 1723

Network TheoryAC Circuit Analysis

The average value of a pure sinusoidal voltage over one complete cycle is?

AIts RMS value
BIts peak value
CZero
DPeak divided by two

Show AnswerHide Answer Report an error

Correct Answer: C. Zero

Explanation: Positive and negative half-cycle areas cancel, so the average over a full cycle is zero.

Reference: Standard network theory: sinusoidal average value

Question 1724

Network TheoryAC Circuit Analysis

For an impedance Z=3-j4 ohm, the magnitude of Z is?

A1 ohm
B5 ohm
C7 ohm
D25 ohm

Show AnswerHide Answer Report an error

Correct Answer: B. 5 ohm

Explanation: |Z|=sqrt(3^2+(-4)^2)=5 ohm.

Reference: Standard network theory: complex impedance numerical

Question 1725

Network TheoryAC Circuit Analysis

For Z=3-j4 ohm, the impedance angle is closest to?

A-53.1 degrees
B+53.1 degrees
C-36.9 degrees
D+36.9 degrees

Show AnswerHide Answer Report an error

Correct Answer: A. -53.1 degrees

Explanation: The angle is tan^-1(-4/3)≈-53.1 degrees, indicating capacitive behavior.

Reference: Standard network theory: impedance phase numerical

Question 1726

Network TheoryAC Circuit Analysis

An admittance is Y=0.04+j0.03 S. Its magnitude is?

A0.01 S
B0.05 S
C0.07 S
D0.12 S

Show AnswerHide Answer Report an error

Correct Answer: B. 0.05 S

Explanation: |Y|=sqrt(0.04^2+0.03^2)=0.05 S.

Reference: Standard network theory: admittance magnitude numerical

Question 1727

Network TheoryAC Power

A load draws 10 A RMS from a 200 V RMS supply at power factor 0.6 lagging. Its real power is?

A600 W
B1200 W
C1600 W
D2000 W

Show AnswerHide Answer Report an error

Correct Answer: B. 1200 W

Explanation: P=VI cos(phi)=200×10×0.6=1200 W.

Reference: Standard network theory: single-phase real power numerical

Question 1728

Network TheoryAC Power

For the same 200 V, 10 A, 0.6 lagging load, the reactive power magnitude is?

A800 var
B1200 var
C1600 var
D2000 var

Show AnswerHide Answer Report an error

Correct Answer: C. 1600 var

Explanation: sin(phi)=sqrt(1-0.6^2)=0.8, so Q=VI sin(phi)=200×10×0.8=1600 var.

Reference: Standard network theory: single-phase reactive power numerical

Question 1729

Network TheoryAC Power

A load consumes 3 kW and 4 kVAR. Its apparent power magnitude is?

A1 kVA
B5 kVA
C7 kVA
D12 kVA

Show AnswerHide Answer Report an error

Correct Answer: B. 5 kVA

Explanation: |S|=sqrt(P^2+Q^2)=sqrt(3^2+4^2)=5 kVA.

Reference: Standard network theory: complex power triangle numerical

Question 1730

Network TheoryThree-Phase Circuits

A balanced three-phase delta-connected load has a phase current of 8 A. The line current magnitude is approximately?

A4.62 A
B8 A
C13.86 A
D24 A

Show AnswerHide Answer Report an error

Correct Answer: C. 13.86 A

Explanation: For a balanced delta connection, IL=sqrt(3)Iph≈1.732×8=13.86 A.

Reference: Standard network theory: delta line current numerical

Question 1731

Network TheoryThree-Phase Circuits

For a balanced three-phase delta-connected load, the phase voltage is related to line voltage by?

AVph=VL
BVph=VL/sqrt(3)
CVph=sqrt(3)VL
DVph=3VL

Show AnswerHide Answer Report an error

Correct Answer: A. Vph=VL

Explanation: In a balanced delta connection, each phase is connected directly across two lines, so phase voltage equals line voltage.

Reference: Standard network theory: delta connection

Question 1732

Network TheoryThree-Phase Circuits

A balanced three-phase star load has line current 12 A. The phase current is?

A4 A
B6.93 A
C12 A
D20.78 A

Show AnswerHide Answer Report an error

Correct Answer: C. 12 A

Explanation: In a star connection, line current equals phase current, so Iph=IL=12 A.

Reference: Standard network theory: star line and phase current

Question 1733

Network TheoryThree-Phase Circuits

A balanced three-phase system supplies 10 kW at 400 V line voltage and unity power factor. The line current is closest to?

A8.33 A
B14.43 A
C25 A
D43.3 A

Show AnswerHide Answer Report an error

Correct Answer: B. 14.43 A

Explanation: P=sqrt(3)VLILcos(phi). At unity power factor, IL=10000/(1.732×400)≈14.43 A.

Reference: Standard network theory: three-phase current numerical

Question 1734

Network TheoryThree-Phase Circuits

A balanced three-phase load takes 6 kW at a power factor of 0.6 lagging. Its reactive power is?

A3.6 kVAR
B4.8 kVAR
C6 kVAR
D8 kVAR

Show AnswerHide Answer Report an error

Correct Answer: D. 8 kVAR

Explanation: For cos(phi)=0.6, sin(phi)=0.8 and tan(phi)=4/3. Hence Q=P tan(phi)=6×4/3=8 kVAR.

Reference: Standard network theory: three-phase reactive power

Question 1735

Network TheoryThree-Phase Circuits

In the two-wattmeter method for a balanced three-phase load, total real power is equal to?

AW1-W2
BW1+W2
Csqrt(3)(W1+W2)
D3(W1-W2)

Show AnswerHide Answer Report an error

Correct Answer: B. W1+W2

Explanation: For a balanced three-phase load measured by the two-wattmeter method, total real power is the algebraic sum W1+W2.

Reference: Standard network theory: two-wattmeter method

Question 1736

Network TheoryThree-Phase Circuits

In the two-wattmeter method, if the balanced load has unity power factor, the two wattmeters ideally read?

AEqual positive values
BEqual and opposite values
COne zero and one positive value
DBoth zero

Show AnswerHide Answer Report an error

Correct Answer: A. Equal positive values

Explanation: At unity power factor phi=0, the readings are proportional to cos(30°-phi) and cos(30°+phi), so they are equal and positive.

Reference: Standard network theory: two-wattmeter unity power factor

Question 1737

Network TheoryThree-Phase Circuits

In the two-wattmeter method for a balanced load, one wattmeter reads zero when the power factor is?

A1
B0.866
C0.5
D0

Show AnswerHide Answer Report an error

Correct Answer: C. 0.5

Explanation: One reading becomes zero at phi=60°, for which cos(phi)=0.5.

Reference: Standard network theory: two-wattmeter power factor

Question 1738

Network TheoryThree-Phase Circuits

A balanced three-phase load is measured by two wattmeters reading 4 kW and 2 kW. The total real power is?

A2 kW
B4 kW
C6 kW
D8 kW

Show AnswerHide Answer Report an error

Correct Answer: C. 6 kW

Explanation: Total three-phase real power in the two-wattmeter method is W1+W2=4+2=6 kW.

Reference: Standard network theory: two-wattmeter numerical

Question 1739

Network TheoryAC Power

For a sinusoidal steady-state circuit, complex power S is conventionally written as?

AP-jQ
BP+jQ
CQ+jP
DP/Q

Show AnswerHide Answer Report an error

Correct Answer: B. P+jQ

Explanation: Complex power is S=P+jQ, where P is average real power and Q is reactive power.

Reference: Standard network theory: complex power

Question 1740

Network TheoryAC Power

A load has complex power S=3+j4 kVA. Its power factor is?

A0.4 lagging
B0.6 lagging
C0.8 lagging
D1.0

Show AnswerHide Answer Report an error

Correct Answer: B. 0.6 lagging

Explanation: |S|=5 kVA and power factor=P/|S|=3/5=0.6. Positive Q denotes an inductive, lagging load.

Reference: Standard network theory: complex power factor numerical

Question 1741

Network TheoryAC Power

A load has complex power S=4-j3 kVA. Its power factor characteristic is?

A0.8 leading
B0.8 lagging
C0.6 leading
D0.6 lagging

Show AnswerHide Answer Report an error

Correct Answer: A. 0.8 leading

Explanation: |S|=5 kVA, so pf=4/5=0.8. Negative reactive power indicates capacitive behavior, hence leading power factor.

Reference: Standard network theory: leading power factor

Question 1742

Network TheoryLaplace Transform

The initial-value theorem for a function f(t) with suitable transform F(s) gives f(0+) as?

Alim s->0 of sF(s)
Blim s->infinity of sF(s)
Clim s->0 of F(s)/s
Dlim s->infinity of F(s)/s

Show AnswerHide Answer Report an error

Correct Answer: B. lim s->infinity of sF(s)

Explanation: Under the theorem's applicability conditions, f(0+)=lim as s approaches infinity of sF(s).

Reference: Standard network theory: initial-value theorem

Question 1743

Network TheoryLaplace Transform

If F(s)=5/[s(s+5)], the initial value f(0+) obtained using the initial-value theorem is?

Show AnswerHide Answer Report an error

Correct Answer: A. 0

Explanation: f(0+)=lim s->infinity sF(s)=lim 5/(s+5)=0.

Reference: Standard network theory: initial-value theorem numerical

Question 1744

Network TheoryLaplace Transform

The final-value theorem gives f(infinity), when applicable, as?

Alim s->infinity sF(s)
Blim s->0 sF(s)
Clim s->0 F(s)/s
Dlim s->infinity F(s)

Show AnswerHide Answer Report an error

Correct Answer: B. lim s->0 sF(s)

Explanation: If the required pole conditions are satisfied, f(infinity)=lim as s approaches zero of sF(s).

Reference: Standard network theory: final-value theorem

Question 1745

Network TheoryLaplace Transform

The final-value theorem is not valid for a response whose sF(s) has?

AAll poles strictly in the left-half plane
BA pole in the right-half plane
CNo finite poles
DOnly negative real poles

Show AnswerHide Answer Report an error

Correct Answer: B. A pole in the right-half plane

Explanation: A right-half-plane pole produces a growing mode, so the response does not approach a finite final value and the final-value theorem cannot be used in its standard form.

Reference: Standard network theory: final-value theorem applicability

Question 1746

Network TheoryTransient Analysis

The natural response of a linear circuit is produced by?

AStored energy and initial conditions with independent sources set to zero
BIndependent sources only with all stored energy removed
COnly sinusoidal sources
DOnly dependent sources removed

Show AnswerHide Answer Report an error

Correct Answer: A. Stored energy and initial conditions with independent sources set to zero

Explanation: The natural or zero-input response is due to energy initially stored in capacitors and inductors after independent sources are set to zero.

Reference: Standard network theory: natural response

Question 1747

Network TheoryTransient Analysis

The zero-state response of a linear circuit is the response when?

AAll independent sources are zero but initial energy is retained
BInitial conditions are zero and external sources act
CBoth sources and initial conditions are zero
DOnly dependent sources are removed

Show AnswerHide Answer Report an error

Correct Answer: B. Initial conditions are zero and external sources act

Explanation: Zero-state response is caused by external excitation with all independent initial energy-storage conditions set to zero.

Reference: Standard network theory: zero-state response

Question 1748

Network TheoryTransient Analysis

The complete response of a linear circuit can be expressed as?

ANatural response plus forced response
BResistance plus reactance only
CVoltage response minus current response
DInitial value multiplied by final value

Show AnswerHide Answer Report an error

Correct Answer: A. Natural response plus forced response

Explanation: A linear circuit's complete response is commonly decomposed into natural (transient) and forced components.

Reference: Standard network theory: complete response

Question 1749

Network TheoryTransient Analysis

For a stable first-order circuit excited by a constant DC source, the natural-response component as t approaches infinity?

AGrows without bound
BApproaches zero
CBecomes equal to the source voltage in every circuit
DOscillates indefinitely

Show AnswerHide Answer Report an error

Correct Answer: B. Approaches zero

Explanation: A stable first-order natural term has the form Ke^(-t/tau), which decays to zero as time increases.

Reference: Standard network theory: natural response decay

Question 1750

Network TheoryTransient Analysis

A first-order circuit has time constant 50 ms. After 150 ms, its natural-response magnitude is approximately what percentage of its initial value?

A36.8%
B13.5%
C5.0%
D0.67%

Show AnswerHide Answer Report an error

Correct Answer: C. 5.0%

Explanation: 150 ms equals 3 time constants. e^-3≈0.0498, so about 5% remains.

Reference: Standard network theory: exponential decay numerical

Question 1751

Network TheorySecond-Order Circuits

For a series RLC circuit, the condition R^2<4L/C corresponds to which natural-response type?

AOverdamped
BCritically damped
CUnderdamped
DFirst-order

Show AnswerHide Answer Report an error

Correct Answer: C. Underdamped

Explanation: For series RLC, alpha=R/(2L) and omega0=1/sqrt(LC). The inequality R^2<4L/C is equivalent to alpha<omega0, giving an underdamped response.

Reference: Standard network theory: RLC damping condition

Question 1752

Network TheorySecond-Order Circuits

For a series RLC circuit, critical damping occurs at resistance R equal to?

Asqrt(L/C)
B2sqrt(L/C)
Csqrt(C/L)
D2sqrt(C/L)

Show AnswerHide Answer Report an error

Correct Answer: B. 2sqrt(L/C)

Explanation: Critical damping requires R/(2L)=1/sqrt(LC), which gives R=2sqrt(L/C).

Reference: Standard network theory: critical resistance

Question 1753

Network TheorySecond-Order Circuits

A series RLC circuit has L=1 H and C=0.25 F. The resistance required for critical damping is?

A1 ohm
B2 ohm
C4 ohm
D8 ohm

Show AnswerHide Answer Report an error

Correct Answer: C. 4 ohm

Explanation: Rcrit=2sqrt(L/C)=2sqrt(1/0.25)=2×2=4 ohm.

Reference: Standard network theory: critical resistance numerical

Question 1754

Network TheorySecond-Order Circuits

In an overdamped second-order circuit, the characteristic roots are typically?

ATwo distinct negative real roots for a stable passive circuit
BA repeated imaginary pair
CA complex-conjugate pair with zero real part
DOne root only at the origin

Show AnswerHide Answer Report an error

Correct Answer: A. Two distinct negative real roots for a stable passive circuit

Explanation: Overdamping gives two distinct real roots; in a stable passive circuit both are negative and produce nonoscillatory decaying exponentials.

Reference: Standard network theory: overdamped roots

Question 1755

Network TheorySecond-Order Circuits

In a critically damped second-order circuit, the natural response contains terms of the form?

A(A+Bt)e^(-alpha t)
BA sin(alpha t) only
CAe^(+alpha t) only
DA+Bt with no exponential

Show AnswerHide Answer Report an error

Correct Answer: A. (A+Bt)e^(-alpha t)

Explanation: A repeated real characteristic root at -alpha produces the natural-response form (A+Bt)e^(-alpha t).

Reference: Standard network theory: critically damped response

Question 1756

Network TheoryNetwork Duality

In network duality, the dual quantity corresponding to voltage is?

ACurrent
BResistance
CPower
DCharge only

Show AnswerHide Answer Report an error

Correct Answer: A. Current

Explanation: In a dual network, voltage and current interchange roles, just as KVL and KCL interchange.

Reference: Standard network theory: duality

Question 1757

Network TheoryNetwork Duality

In network duality, a series connection in the original network corresponds to what in the dual network?

AAnother series connection only
BA parallel connection
CAn open circuit only
DA dependent source only

Show AnswerHide Answer Report an error

Correct Answer: B. A parallel connection

Explanation: Series and parallel connections are dual concepts.

Reference: Standard network theory: series-parallel duality

Question 1758

Network TheoryNetwork Duality

The dual of resistance R is represented by which network quantity under the usual normalized duality correspondence?

AConductance G
BInductance L
CCapacitance C
DReactance only

Show AnswerHide Answer Report an error

Correct Answer: A. Conductance G

Explanation: Resistance and conductance are dual quantities because voltage-current and series-parallel roles are interchanged.

Reference: Standard network theory: resistance-conductance duality

Question 1759

Network TheoryNetwork Duality

Under network duality, an inductor is dual to a?

AResistor
BCapacitor
CVoltage source
DTransformer

Show AnswerHide Answer Report an error

Correct Answer: B. Capacitor

Explanation: Inductance and capacitance are dual energy-storage elements.

Reference: Standard network theory: inductor-capacitor duality

Question 1760

Network TheoryNetwork Duality

The dual of Kirchhoff’s voltage law is?

AOhm's law
BKirchhoff's current law
CFaraday's law
DMaximum power theorem

Show AnswerHide Answer Report an error

Correct Answer: B. Kirchhoff's current law

Explanation: KVL constrains loop voltages, while its dual KCL constrains node currents.

Reference: Standard network theory: KVL-KCL duality

Question 1761

Network TheoryNetwork Theorems

The substitution theorem permits a branch of a network to be replaced by another element or source provided the replacement maintains the same?

ABranch voltage and current
BTotal number of nodes only
COperating frequency only
DPower factor of every other branch only

Show AnswerHide Answer Report an error

Correct Answer: A. Branch voltage and current

Explanation: At a specified operating condition, substitution is valid when the replacement preserves the original branch terminal voltage and current.

Reference: Standard network theory: substitution theorem

Question 1762

Network TheoryNetwork Theorems

The compensation theorem is useful for determining changes in network currents and voltages caused by a change in?

AA branch impedance
BThe number of graph nodes only
CSource frequency with every impedance fixed
DReference-node labeling

Show AnswerHide Answer Report an error

Correct Answer: A. A branch impedance

Explanation: The compensation theorem evaluates incremental response when a branch impedance changes in a linear bilateral network.

Reference: Standard network theory: compensation theorem

Question 1763

Network TheoryNetwork Theorems

If a branch carrying current I has its impedance increased by Delta Z, the compensating source magnitude used in the compensation theorem is proportional to?

AI/Delta Z
BI Delta Z
CI squared divided by Delta Z
DDelta Z/I squared

Show AnswerHide Answer Report an error

Correct Answer: B. I Delta Z

Explanation: The compensating voltage magnitude is I Delta Z, with polarity chosen according to the theorem's replacement convention.

Reference: Standard network theory: compensation theorem relation

Question 1764

Network TheoryNetwork Synthesis

For a polynomial to be Hurwitz, all of its roots must lie in which region, allowing simple j-omega-axis roots only under the standard special conditions?

AClosed left-half plane
BOpen right-half plane
COnly positive real axis
DOnly at the origin

Show AnswerHide Answer Report an error

Correct Answer: A. Closed left-half plane

Explanation: A Hurwitz polynomial has no roots in the open right-half plane; permitted imaginary-axis roots are simple under the standard network-synthesis definition.

Reference: Standard network theory: Hurwitz polynomial

Question 1765

Network TheoryNetwork Synthesis

Which polynomial is Hurwitz?

As^2-3s+2
Bs^2+3s+2
Cs^2-1
Ds^2-2s+5

Show AnswerHide Answer Report an error

Correct Answer: B. s^2+3s+2

Explanation: s^2+3s+2=(s+1)(s+2), whose roots -1 and -2 lie in the left-half plane.

Reference: Standard network theory: Hurwitz polynomial numerical

Question 1766

Network TheoryNetwork Synthesis

For a positive-real rational function, any poles on the j-omega axis must be?

AMultiple with complex residues
BSimple with real nonnegative residues
CAlways double poles
DLocated only in the right-half plane

Show AnswerHide Answer Report an error

Correct Answer: B. Simple with real nonnegative residues

Explanation: A positive-real function may have simple imaginary-axis poles, and their residues must be real and nonnegative.

Reference: Standard network theory: positive-real pole condition

Question 1767

Network TheoryNetwork Synthesis

For a positive-real function F(s), complex poles and zeros must occur in?

AUnrelated locations
BComplex-conjugate pairs
COnly the right-half plane
DOnly at s=0

Show AnswerHide Answer Report an error

Correct Answer: B. Complex-conjugate pairs

Explanation: Because a positive-real network function is real for real s, nonreal poles and zeros occur in complex-conjugate pairs.

Reference: Standard network theory: conjugate roots

Question 1768

Network TheoryNetwork Synthesis

An RC driving-point impedance has poles and zeros on the negative real axis that characteristically?

AInterlace
BAlways coincide
CAppear only as complex pairs
DLie only on the positive real axis

Show AnswerHide Answer Report an error

Correct Answer: A. Interlace

Explanation: For an RC driving-point impedance, realizability imposes alternating or interlacing negative-real poles and zeros with the appropriate ordering.

Reference: Standard network theory: RC impedance synthesis

Question 1769

Network TheoryNetwork Synthesis

For an RL driving-point impedance, poles and zeros of a realizable simple ladder form are characteristically located on the?

APositive real axis
BNegative real axis
Cj-omega axis only
DUnit circle

Show AnswerHide Answer Report an error

Correct Answer: B. Negative real axis

Explanation: RL driving-point functions have real nonpositive critical frequencies; their finite poles and zeros interlace on the negative real axis.

Reference: Standard network theory: RL impedance synthesis

Question 1770

Network TheoryNetwork Synthesis

A Foster realization is especially associated with expansion of a driving-point function into?

APartial fractions
BA Fourier series only
CA determinant of the incidence matrix
DA power series in time

Show AnswerHide Answer Report an error

Correct Answer: A. Partial fractions

Explanation: Foster synthesis decomposes an immittance into partial-fraction terms that map to simple circuit sections.

Reference: Standard network theory: Foster synthesis principle

Question 1771

Network TheoryNetwork Synthesis

In Cauer-I synthesis of a driving-point impedance, continued-fraction extraction generally begins with behavior near?

As=infinity
Bs=1 only
Ct=0 in the time domain
DThe load current zero crossing

Show AnswerHide Answer Report an error

Correct Answer: A. s=infinity

Explanation: Cauer-I realization is obtained by continued-fraction expansion about infinity, successively extracting ladder elements.

Reference: Standard network theory: Cauer-I synthesis

Question 1772

Network TheoryNetwork Synthesis

In Cauer-II synthesis, the continued-fraction expansion is associated with behavior near?

As=0
Bs=infinity only
Cs=j only
Dt=infinity directly

Show AnswerHide Answer Report an error

Correct Answer: A. s=0

Explanation: Cauer-II form is obtained through continued-fraction expansion about the origin.

Reference: Standard network theory: Cauer-II synthesis

Question 1773

Network TheoryNetwork Synthesis

For a pure reactance one-port made only of ideal L and C elements, the real part of its impedance on the j-omega axis away from poles is?

APositive and frequency dependent
BNegative and frequency dependent
CZero
DAlways equal to 1 ohm

Show AnswerHide Answer Report an error

Correct Answer: C. Zero

Explanation: An ideal lossless LC network absorbs zero average power, so its impedance is purely imaginary away from singularities.

Reference: Standard network theory: reactance function

Question 1774

Network TheoryNetwork Synthesis

If Z(s)=sL is the driving-point impedance of an ideal inductor, Z(0) equals?

A0
BL
C1/L
DInfinity

Show AnswerHide Answer Report an error

Correct Answer: A. 0

Explanation: At s=0, Z(s)=sL becomes zero, consistent with an ideal inductor behaving as a short circuit at DC steady state.

Reference: Standard network theory: inductor driving-point impedance

Question 1775

Network TheoryNetwork Synthesis

If Z(s)=1/(sC) is the driving-point impedance of an ideal capacitor, the magnitude of Z(s) as s approaches zero tends to?

AZero
BC
C1/C
DInfinity

Show AnswerHide Answer Report an error

Correct Answer: D. Infinity

Explanation: As s approaches zero, 1/(sC) becomes unbounded, consistent with a capacitor acting as an open circuit at DC steady state.

Reference: Standard network theory: capacitor driving-point impedance

Question 1776

Network TheoryNetwork Functions

For a passive one-port, the driving-point admittance Y(s) is the reciprocal of?

ADriving-point impedance Z(s)
BTransfer impedance only
CLoop-current matrix
DIncidence determinant only

Show AnswerHide Answer Report an error

Correct Answer: A. Driving-point impedance Z(s)

Explanation: At the same port, Y(s)=I(s)/V(s)=1/Z(s), provided the reciprocal is defined.

Reference: Standard network theory: driving-point immittance

Question 1777

Network TheoryNetwork Functions

A zero of a driving-point impedance Z(s) becomes what in the corresponding admittance Y(s)=1/Z(s), assuming no cancellation?

AA zero
BA pole
CA constant
DA branch current source

Show AnswerHide Answer Report an error

Correct Answer: B. A pole

Explanation: Taking the reciprocal interchanges poles and zeros, so a zero of Z becomes a pole of Y.

Reference: Standard network theory: impedance-admittance poles and zeros

Question 1778

Network TheoryNetwork Functions

If Z(s)=(s+2)/(s+5), the corresponding admittance Y(s) is?

A(s+2)/(s+5)
B(s+5)/(s+2)
C1/[(s+2)(s+5)]
Ds+7

Show AnswerHide Answer Report an error

Correct Answer: B. (s+5)/(s+2)

Explanation: Admittance is the reciprocal of impedance, hence Y(s)=(s+5)/(s+2).

Reference: Standard network theory: immittance conversion numerical

Question 1779

Network TheoryNetwork Synthesis

A rational function whose numerator degree exceeds its denominator degree by more than one cannot directly represent the driving-point impedance of a finite passive RLC network because it violates the usual?

APositive-real realizability requirements
BKCL sign convention only
CNode numbering rule
DTransformer turns-ratio rule

Show AnswerHide Answer Report an error

Correct Answer: A. Positive-real realizability requirements

Explanation: Finite passive RLC driving-point immittances are positive-real rational functions with constrained high-frequency behavior; an excessive degree difference is incompatible with those realizability conditions.

Reference: Standard network theory: realizability condition

Question 1780

Network TheoryNetwork Synthesis

For a positive-real function F(s), the real part Re[F(j omega)] at frequencies where F is finite must be?

ANonnegative
BStrictly negative
CAlways zero
DPurely imaginary

Show AnswerHide Answer Report an error

Correct Answer: A. Nonnegative

Explanation: A key boundary property of a positive-real function is Re[F(j omega)]>=0 wherever the function is finite.

Reference: Standard network theory: positive-real frequency-axis condition

Question 1781

Network TheoryMatrix Network Analysis

For a network with node-voltage vector V and nodal admittance matrix Y, the standard matrix equation is?

AYV=I
BYI=V
CVY=I squared
DY+V=I

Show AnswerHide Answer Report an error

Correct Answer: A. YV=I

Explanation: Nodal analysis in matrix form is YV=I, where I is the vector of externally injected node currents.

Reference: Standard network theory: nodal admittance matrix

Question 1782

Network TheoryMatrix Network Analysis

In a passive reciprocal resistive network, the nodal admittance matrix is typically?

ASkew-symmetric
BSymmetric
CAlways diagonal
DSingular after choosing a reference node in every case

Show AnswerHide Answer Report an error

Correct Answer: B. Symmetric

Explanation: For a reciprocal resistive network, mutual admittance terms satisfy symmetry, so the reduced nodal admittance matrix is symmetric.

Reference: Standard network theory: reciprocal nodal matrix

Question 1783

Network TheoryMatrix Network Analysis

In a nodal admittance matrix, a diagonal element Yii is generally formed from?

AThe negative sum of all conductances incident at node i
BThe sum of conductances connected to node i
COnly the largest branch resistance
DThe product of all branch impedances

Show AnswerHide Answer Report an error

Correct Answer: B. The sum of conductances connected to node i

Explanation: The diagonal entry is the sum of admittances incident on the corresponding node under the standard nodal formulation.

Reference: Standard network theory: nodal matrix diagonal

Question 1784

Network TheoryMatrix Network Analysis

For two distinct nodes i and j directly connected by admittance y, the off-diagonal nodal-matrix entries Yij and Yji are normally?

A+y
B+2y
C-y
D1/y

Show AnswerHide Answer Report an error

Correct Answer: C. -y

Explanation: Under the standard nodal convention, a branch admittance between two non-reference nodes contributes -y to the corresponding off-diagonal entries.

Reference: Standard network theory: nodal matrix off-diagonal

Question 1785

Network TheoryMatrix Network Analysis

A two-node reduced nodal matrix is [[5,-2],[-2,4]] siemens. If the injected-current vector is [6,2] A, which equations are correct?

A5V1-2V2=6 and -2V1+4V2=2
B5V1+2V2=6 and 2V1+4V2=2
C5V1-2V2=2 and -2V1+4V2=6
DV1+V2=8 only

Show AnswerHide Answer Report an error

Correct Answer: A. 5V1-2V2=6 and -2V1+4V2=2

Explanation: Direct multiplication of YV=I gives 5V1-2V2=6 and -2V1+4V2=2.

Reference: Standard network theory: nodal matrix numerical

Question 1786

Network TheoryMatrix Network Analysis

For the equations 5V1-2V2=6 and -2V1+4V2=2, the node voltage V1 is?

A1.00 V
B1.75 V
C2.25 V
D3.50 V

Show AnswerHide Answer Report an error

Correct Answer: B. 1.75 V

Explanation: Solving simultaneously: the second equation gives V1=2V2-1. Substitution yields V2=1.375 V, hence V1=1.75 V.

Reference: Standard network theory: nodal matrix solution numerical

Question 1787

Network TheoryTwo-Port Networks

A reciprocal two-port has z12=3 ohm. What must z21 be?

A-3 ohm
B0 ohm
C3 ohm
D1/3 siemens

Show AnswerHide Answer Report an error

Correct Answer: C. 3 ohm

Explanation: Reciprocity in z-parameters requires z12=z21, hence z21=3 ohm.

Reference: Standard network theory: z-parameter reciprocity numerical

Question 1788

Network TheoryTwo-Port Networks

A symmetrical two-port has z11=8 ohm. What must z22 be?

A0 ohm
B4 ohm
C8 ohm
D16 ohm

Show AnswerHide Answer Report an error

Correct Answer: C. 8 ohm

Explanation: For a symmetrical two-port represented by z-parameters, z11=z22.

Reference: Standard network theory: z-parameter symmetry numerical

Question 1789

Network TheoryTwo-Port Networks

For a two-port with z11=6 ohm, z12=z21=2 ohm and z22=5 ohm, the determinant of the z-parameter matrix is?

A14 ohm squared
B26 ohm squared
C30 ohm squared
D34 ohm squared

Show AnswerHide Answer Report an error

Correct Answer: B. 26 ohm squared

Explanation: The determinant is z11z22-z12z21=6×5-2×2=26 ohm squared.

Reference: Standard network theory: z-matrix determinant numerical

Question 1790

Network TheoryTwo-Port Networks

If a two-port z-parameter matrix has determinant Delta_z, the y-parameter matrix, when the inverse exists, is obtained by?

AMultiplying every z-entry by Delta_z
BMatrix inversion of Z
CAdding the four z-parameters
DTransposing Z only

Show AnswerHide Answer Report an error

Correct Answer: B. Matrix inversion of Z

Explanation: The admittance matrix is Y=Z^{-1}, provided det(Z) is nonzero.

Reference: Standard network theory: z-to-y conversion

Question 1791

Network TheoryTwo-Port Networks

For Z=[[4,2],[2,3]] ohm, the element y11 of Y=Z^{-1} is?

A0.125 S
B0.25 S
C0.375 S
D0.50 S

Show AnswerHide Answer Report an error

Correct Answer: C. 0.375 S

Explanation: det(Z)=4×3-2×2=8. Z^{-1}=(1/8)[[3,-2],[-2,4]], so y11=3/8=0.375 S.

Reference: Standard network theory: z-to-y conversion numerical

Question 1792

Network TheoryTwo-Port Networks

For the same Z=[[4,2],[2,3]] ohm, the transfer admittance y12 is?

A-0.25 S
B+0.25 S
C-0.50 S
D+0.50 S

Show AnswerHide Answer Report an error

Correct Answer: A. -0.25 S

Explanation: From Z^{-1}=(1/8)[[3,-2],[-2,4]], y12=-2/8=-0.25 S.

Reference: Standard network theory: transfer admittance numerical

Question 1793

Network TheoryNetwork Functions

A pole of multiplicity two at s=-a produces a time-domain natural-response term containing?

AOnly e^(-at)
Bt e^(-at) in addition to e^(-at)
Csin(at) only
DA constant only

Show AnswerHide Answer Report an error

Correct Answer: B. t e^(-at) in addition to e^(-at)

Explanation: A repeated pole of order two generates terms proportional to e^(-at) and t e^(-at).

Reference: Standard network theory: repeated poles

Question 1794

Network TheoryNetwork Functions

A complex-conjugate pole pair at s=-2 plus or minus j5 produces a natural response with an envelope proportional to?

Ae^(+2t)
Be^(-2t)
Ce^(-5t)
DA constant

Show AnswerHide Answer Report an error

Correct Answer: B. e^(-2t)

Explanation: The real part of the poles determines the exponential envelope, so the oscillation decays as e^(-2t).

Reference: Standard network theory: complex poles

Question 1795

Network TheoryNetwork Functions

A transfer function has poles at -1 and -10. Which pole normally dominates the long-time response if its mode is present?

APole at -10
BPole at -1
CBoth always decay at identical rates
DNeither pole affects settling

Show AnswerHide Answer Report an error

Correct Answer: B. Pole at -1

Explanation: The pole closest to the imaginary axis, -1, has the slowest exponential decay and therefore dominates the long-time response.

Reference: Standard network theory: dominant pole

Question 1796

Network TheoryNetwork Functions

For H(s)=10/[(s+1)(s+10)], the DC gain is?

A0.1
B1
C10
D100

Show AnswerHide Answer Report an error

Correct Answer: B. 1

Explanation: H(0)=10/(1×10)=1.

Reference: Standard network theory: DC gain numerical

Question 1797

Network TheoryNetwork Functions

For H(s)=K/[(s+2)(s+5)], what value of K gives a DC gain of 1?

Show AnswerHide Answer Report an error

Correct Answer: C. 10

Explanation: H(0)=K/(2×5)=K/10. Setting H(0)=1 gives K=10.

Reference: Standard network theory: normalized DC gain numerical

Question 1798

Network TheoryNetwork Functions

For H(s)=(s+4)/(s+8), the high-frequency gain approaches?

A0
B0.5
C1
D4

Show AnswerHide Answer Report an error

Correct Answer: C. 1

Explanation: The numerator and denominator have equal degree and equal leading coefficients, so the limit as |s| tends to infinity is 1.

Reference: Standard network theory: high-frequency gain numerical

Question 1799

Network TheoryNetwork Functions

A network function has a pole at the origin. Its corresponding natural mode includes which behavior?

AA nondecaying constant term
BOnly an exponentially decaying term
COnly a growing sinusoid
DNo time-domain contribution

Show AnswerHide Answer Report an error

Correct Answer: A. A nondecaying constant term

Explanation: A simple pole at s=0 corresponds to a constant time-domain mode rather than an exponentially decaying mode.

Reference: Standard network theory: pole at origin

Question 1800

Network TheoryNetwork Functions

For F(s)=1/[s(s+2)], the residue associated with the pole at s=0 is?

A0
B0.5
C1
D2

Show AnswerHide Answer Report an error

Correct Answer: B. 0.5

Explanation: For a simple pole at zero, the residue is lim(s->0) sF(s)=1/(s+2)|s=0=1/2.

Reference: Standard network theory: residue numerical