Second-Order Circuits MCQs

Practice Second-Order Circuits MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1

Network TheorySecond-Order Circuits

A series RLC circuit has R = 10 ohm, L = 0.1 H and C = 100 microfarad. Its damping factor alpha = R/(2L) is?

A5 s^-1
B50 s^-1
C100 s^-1
D500 s^-1

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Correct Answer: B. 50 s^-1

Explanation: alpha=R/(2L)=10/(0.2)=50 s^-1.

Reference: Standard network theory: second-order circuits

Question 2

Network TheorySecond-Order Circuits

For the same RLC circuit with L = 0.1 H and C = 100 microfarad, the undamped natural angular frequency omega0 = 1/sqrt(LC) is?

A100 rad/s
B316.2 rad/s
C1000 rad/s
D3162 rad/s

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Correct Answer: B. 316.2 rad/s

Explanation: LC=0.1×100×10^-6=10^-5, so omega0=1/sqrt(10^-5)≈316.2 rad/s.

Reference: Standard network theory: second-order circuits

Question 3

Network TheorySecond-Order Circuits

A series RLC natural response is underdamped when?

Aalpha is less than omega0
Balpha equals omega0
Calpha is greater than omega0
DR is always zero only

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Correct Answer: A. alpha is less than omega0

Explanation: The second-order response is underdamped when alphaomega0.

Reference: Standard network theory: second-order circuits

Question 4

Network TheorySecond-Order Circuits

Critical damping in a second-order series RLC circuit occurs when?

Aalpha=0
Balpha=omega0
Calpha=2omega0
Domega0=0

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Correct Answer: B. alpha=omega0

Explanation: Critical damping occurs at the boundary between oscillatory and nonoscillatory responses, where alpha equals omega0.

Reference: Standard network theory: second-order circuits

Question 5

Network TheorySecond-Order Circuits

A second-order characteristic equation is s^2 + 6s + 25 = 0. Comparing with s^2 + 2 zeta omega_n s + omega_n^2, the natural frequency omega_n is?

A5 rad/s
B6 rad/s
C12.5 rad/s
D25 rad/s

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Correct Answer: A. 5 rad/s

Explanation: omega_n^2=25, so omega_n=5 rad/s.

Reference: Standard network theory: second-order circuits

Question 6

Network TheorySecond-Order Circuits

For s^2 + 6s + 25 = 0, the damping ratio zeta is?

A0.3
B0.6
C1.2
D5

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Correct Answer: B. 0.6

Explanation: 2 zeta omega_n=6 and omega_n=5, so zeta=6/(2×5)=0.6.

Reference: Standard network theory: second-order circuits

Question 7

Network TheorySecond-Order Circuits

A second-order network with damping ratio zeta = 0.6 is?

AUndamped
BUnderdamped
CCritically damped
DOverdamped

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Correct Answer: B. Underdamped

Explanation: A second-order system is underdamped when 0<zeta<1.

Reference: Standard network theory: second-order circuits

Question 8

Network TheorySecond-Order Circuits

For an underdamped second-order network, the damped natural frequency omega_d equals?

Aalpha+omega0
Bsqrt(omega0^2-alpha^2)
Csqrt(alpha^2+omega0^2)
Domega0/alpha

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Correct Answer: B. sqrt(omega0^2-alpha^2)

Explanation: For alpha<omega0, the oscillatory frequency is omega_d=sqrt(omega0^2-alpha^2).

Reference: Standard network theory: damped natural frequency

Question 9

Network TheorySecond-Order Circuits

If omega0=10 rad/s and alpha=6 rad/s, the damped natural frequency is?

A4 rad/s
B6 rad/s
C8 rad/s
D16 rad/s

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Correct Answer: C. 8 rad/s

Explanation: omega_d=sqrt(10^2-6^2)=sqrt(64)=8 rad/s.

Reference: Standard network theory: damped frequency numerical

Question 10

Network TheorySecond-Order Circuits

A series RLC natural response is critically damped when the damping factor alpha and undamped natural frequency omega0 satisfy?

Aalpha=0
Balpha<omega0
Calpha=omega0
Dalpha>omega0

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Correct Answer: C. alpha=omega0

Explanation: Critical damping occurs at the boundary between underdamped and overdamped responses, where alpha=omega0.

Reference: Standard network theory: critical damping

Question 11

Network TheorySecond-Order Circuits

A series RLC circuit has R=4 ohm and L=1 H. Its damping factor alpha is?

A1 rad/s
B2 rad/s
C4 rad/s
D8 rad/s

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Correct Answer: B. 2 rad/s

Explanation: For a series RLC circuit, alpha=R/(2L)=4/(2×1)=2 rad/s.

Reference: Standard network theory: damping factor numerical

Question 12

Network TheorySecond-Order Circuits

For a series RLC circuit with L=1 H and C=0.25 F, the undamped natural frequency omega0 is?

A0.5 rad/s
B1 rad/s
C2 rad/s
D4 rad/s

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Correct Answer: C. 2 rad/s

Explanation: omega0=1/sqrt(LC)=1/sqrt(1×0.25)=2 rad/s.

Reference: Standard network theory: natural frequency numerical

Question 13

Network TheorySecond-Order Circuits

If a second-order network has alpha=2 rad/s and omega0=5 rad/s, its natural response is?

AOverdamped
BCritically damped
CUnderdamped
DNoncausal

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Correct Answer: C. Underdamped

Explanation: Since alpha<omega0, the characteristic roots are complex conjugates and the response is underdamped.

Reference: Standard network theory: damping classification

Question 14

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

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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 15

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)

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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 16

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

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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 17

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

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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 18

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

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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