This set of Instrumentation Transducers Multiple Choice Questions & Answers (MCQs) focuses on “Performance of Systems”.

1. Which of the given statement is true for a zero-order system?

a) Varying transfer function with time

b) Constant transfer function

c) Transfer function = 1/S

d) Transfer function = 1/s^{2}

View Answer

Explanation: Order of a system is the maximum power of ‘S’ in the characteristic equation. For a zero-order system, S will have a power zero and Transfer function will be a constant value.

2. Which of the given factor determines the order of a system?

a) Maximum power of ‘S’ in the characteristic equation

b) Minimum power of ‘S’ in the characteristic equation

c) Value of constant value

d) None of the mentioned

View Answer

Explanation: Maximum power of ‘S’ in the characteristic equation is known as an order of that system. For a zero-order system, power of ‘S’ will be zero and for first-order system maximum power of ‘S’ will be one.

3. Transfer function of a system is given by G(S) = b_{0} ⁄ a_{1}S+a_{0}. What will be the static sensitivity of system?

a) b_{0} ⁄ a_{0}

b) b_{0} ⁄ a_{1}

c) a_{0} ⁄ b_{0}

d) a_{1} ⁄ b_{0}

View Answer

Explanation: Transfer function can be converted into G(S) = K ⁄ (τS+1), in which K is known as static sesistivity of system. Thus K can be expressed as a ratio of b

_{0}and a

_{0}.

4. What will be the time constant for a system represented by transfer function G(S) = 5/(3S+2)?

a) 3

b) 2.5

c) 1.5

d) 2

View Answer

Explanation: Transfer function can be represented as G(S) = K/(τS+1), in which time τ represents time constant.

Time constant=3/2.

5. What will be the damping ratio of a system with transfer function G(S) = 5/(3S^{2}+2S+3)?

a) 1.5

b) 0.5

c) 0.33

d) 2

View Answer

Explanation: Damping ratio of a system with transfer function G(S) = b

_{0}⁄ (a

_{2}S

^{2}+a

_{1}S+a

_{0}), can be found using equation a

_{1}⁄ (2√ a

_{0}a

_{2}). Damping ratio of given system will obtain as 0.333.

6. Which of the following represent condition for an over-damped system?

a) Damping ratio<0

b) Damping ratio=0

c) Damping ratio=0.5

d) Damping ratio>1

View Answer

Explanation: A system with damping ratio ξ greater than 1 is said to be over damped system.

7. Which of the following represents a system with transfer function G(S) = 5/(3S^{2}+8S+3) ?

a) Over damped system

b) Un-damped system

c) Under damped system

d) None of the mentioned

View Answer

Explanation: Damping ratio of a second order system can be found using equation a

_{1}/(2√a

_{0}a

_{2}) which is equal to 1.33. For a damping ratio greater than 1, system will be over damped system.

8. For a ramp input in second order system, which of the following represents the correct relationship between natural frequency and steady state error?

a) Both are directly proportional

b) Both are inversely proportional

c) Both are equal

d) None of the mentioned

View Answer

Explanation: Steady state error for second order system with ramp input can be represented as 2ξK/ω

_{n}, where ωn represents natural frequency.

9. What will be the static sensitivity of a system with transfer function G(S) = 4/(5S^{2}+8S+2)?

a) 0.5

b) 2

c) 4

d) 4/5

View Answer

Explanation: Static sensitivity of a system with transfer function G(S) = b

_{0}/(a

_{2}S

^{2}+a

_{1}S+a

_{0}) can be represented as b

_{0}/a

_{0}.

10. Transfer function of a system with input y(t) = t^{2}/2 is given by 1/S. What will be the obtained output?

a) 6t^{3}

b) t^{3}/6

c) t^{3}

d) t^{4}

View Answer

Explanation: Transfer function of a system is the ratio of output and input of the system in S domain.

Output (in S domain) = Transfer function × Input (in S domain). Output in the time domain can be obtained by finding inverse Laplace transform.

**Sanfoundry Global Education & Learning Series – Instrumentation Transducers.**

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