Root Locus MCQs

Practice Root Locus MCQs with four options, answers and explanations for focused Electronics & Telecommunication Engineering revision.

Question 1

Control SystemsRoot Locus

A root locus shows the locations of closed-loop poles as which quantity varies?

ALoop gain K
BInput amplitude only
CTime variable t
DOutput voltage only

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Correct Answer: A. Loop gain K

Explanation: The root locus traces closed-loop pole locations as a system parameter, conventionally the loop gain K, varies.

Reference: Standard control systems: root locus

Question 2

Control SystemsRoot Locus

Root-locus branches start, for K=0, at the?

AOpen-loop poles
BOpen-loop zeros
CClosed-loop zeros only
DImaginary-axis crossings

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Correct Answer: A. Open-loop poles

Explanation: At zero gain, closed-loop poles coincide with the open-loop poles.

Reference: Standard control systems: root locus

Question 3

Control SystemsRoot Locus

As K approaches infinity, root-locus branches terminate at?

AOpen-loop zeros, including zeros at infinity
BOpen-loop poles only
CThe origin only
DThe positive real axis only

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Correct Answer: A. Open-loop zeros, including zeros at infinity

Explanation: Branches end at finite open-loop zeros; if there are more poles than finite zeros, the remaining branches terminate at zeros at infinity.

Reference: Standard control systems: root locus

Question 4

Control SystemsRoot Locus

The number of root-locus branches equals the number of?

AOpen-loop poles
BOpen-loop finite zeros only
CClosed-loop zeros
DBreakaway points

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Correct Answer: A. Open-loop poles

Explanation: Each open-loop pole is the starting point of one root-locus branch.

Reference: Standard control systems: root locus

Question 5

Control SystemsRoot Locus

If an open-loop transfer function has 3 poles and 1 finite zero, the number of root-locus asymptotes is?

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Correct Answer: B. 2

Explanation: The number of asymptotes is n-m=3-1=2.

Reference: Standard control systems: root locus

Question 6

Control SystemsRoot Locus

On a real-axis segment, a point belongs to the conventional positive-gain root locus if the number of real open-loop poles and zeros to its right is?

AEven
BOdd
CZero only
DAlways two

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Correct Answer: B. Odd

Explanation: For K≥0, a real-axis point lies on the root locus when the total number of real poles and zeros to its right is odd.

Reference: Standard control systems: root locus

Question 7

Control SystemsRoot Locus

A breakaway or break-in point on the real-axis root locus can be found from the gain expression K(s) by solving?

AdK/ds=0
BK=0 only
Cd²K/ds²=0 only
Ds=0 always

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Correct Answer: A. dK/ds=0

Explanation: Candidate real-axis break points are obtained from dK/ds=0 and then checked for validity on the root locus.

Reference: Standard control systems: root locus

Question 8

Control SystemsRoot Locus

For an open-loop transfer function with n poles and m finite zeros, where n>m, the angles of root-locus asymptotes are given by?

A(2q+1)180°/(n-m)
B2q×180°/(n+m)
Cq×90°/n
D180°/(n+m) only

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Correct Answer: A. (2q+1)180°/(n-m)

Explanation: Root-locus asymptote angles are θq=(2q+1)180°/(n-m), q=0,1,...,n-m-1.

Reference: Standard control systems: root locus

Question 9

Control SystemsRoot Locus

The centroid of root-locus asymptotes is located at?

A(sum of poles - sum of zeros)/(n-m)
B(sum of poles + sum of zeros)/(n+m)
CProduct of poles divided by product of zeros
DOrigin in every system

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Correct Answer: A. (sum of poles - sum of zeros)/(n-m)

Explanation: For n>m, the asymptote centroid is σa=(Σpoles-Σzeros)/(n-m).

Reference: Standard control systems: root locus

Question 10

Control SystemsRoot Locus

An open-loop system has poles at 0, -2 and -4 and no finite zeros. The root-locus asymptote centroid is?

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Correct Answer: B. -2

Explanation: σa=[(0-2-4)-0]/3=-6/3=-2.

Reference: Standard control systems: root locus

Question 11

Control SystemsRoot Locus

For the same system with three poles and no finite zeros, the asymptote angles are?

A0°, 120°, 240°
B60°, 180°, 300°
C90°, 180°, 270°
D45°, 180°, 315°

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Correct Answer: B. 60°, 180°, 300°

Explanation: With n-m=3, θq=(2q+1)180°/3 gives 60°, 180° and 300°.

Reference: Standard control systems: root locus