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Measurement & Control - MCQs from AMIE exams (Summer 2018)

Choose the correct answer for the following (10 x 2)

1. A system has the transfer function \frac{5}{{{s^2} + 7s + 4}}. What will be the nature of its unit step response?
(a) overdamped
(b) underdamped
(c) undamped
(d) critically damped

2. A unity feedback system has its open-loop transfer function as \frac{K}{{s({s^2} + s + 2)(s + 3)}}. What will be the range of which system will be stable?
(a) 21/4 > K > 0
(b) 13 > K > 0
(c) 21/44 < K < ∞
(d) -6 < K < ∞

3. Find out the breakaway and break-in points for the transfer function 1 + \frac{{K(s + 2)(s + 3)}}{{s(s + 1)}} = 0
(a) 0, -0.634
(b)  0, -2.366
(c) -2 + √2, -2 - √2
(d) -0.634, -2.366

4. For type-1 plant, with step and ramp inputs, the steady-state errors, are, respectively:
(a) 0, 0
(b) 0, finite
(c) finite, finite
(d) finite, infinite

5. Increase in a gain of the proportional controller results in
(a) increase in peak overshoot, decrease in peak-time.
(b) decrease in peak overshoot, increase in peak time.
(c) increase in both peak; overshoot and peak time.
(d) decrease in both peak overshoot and peak-time.

6. The inductance of a moving iron instrument is given by L = (10 + 5\theta - {\theta ^2})\mu H, where θ is the deflection in radian from zero position. For spring constant (K) = 12 x 10⁻⁶ Nm/rad and current I = 5 A, the deflection (θ) will be:
(a) 20.7⁰
(b) 180°
(c) 90°
(d) 96.8°

7. The electric strength of new insulating oil should have a minimum strength (rms) of 
(a) 30 kV/mm
(b) 3 kV/mm
(c) 50 kN/mm
(d) 5k V/mm

8. Potentiometer sensitivity can be increased by:
(a) decreasing the current in potentiometer wire 
(b) increasing the length of potentiometer wire 
(c) decreasing the length of the potentiometer wire.
(d) replacing the standard cell with a regulated power supply.

9. Which of the following statement is true?
(a) a galvanometer with low resistance in parallel is a voltmeter
(b) a galvanometer with low resistance in series is an ammeter
(c) a galvanometer with high resistance in series is an ammeter
(d) a galvanometer with high resistance in parallel is a voltmeter

10. The dimension of inductance is:
(a) ML²T⁻²I⁻²
(b) ML⁻²T²I²
(c) ML²T⁻²I⁻¹
(d) MLT⁻²I⁻²

Answer

1. (a) 
Compare s2 + 7s + 4 = 0 with s2 + 2ξωn + ωn2 = 0
ωn2 = 4 ⇒ ωn = 2 rad/s and 2ξωn = 7 ⇒ ξ = 7/(2x2) = 1.75
Damping ratio ξ > 1.75 (overdamped)

2. (a)
s(s2 + s + 2) (s + 3) + K = 0
⇒ s4 + 4s3 + 5s2 + 6s + K = 0
Consider the following table


3.5 x 6 - 4K > 0 
⇒ K < 21/4 and K > 0

3. (d)
K = - \frac{{s(s + 1)}}{{(s + 2)(s + 3)}}
For break points
\frac{{dK}}{{ds}} = - \frac{{(2s + 1)(s + 2)(s + 3) - s(s + 1)(2s + 5)}}{{{{[(s + 2)(s + 3)]}^2}}} = 0
Solving we get two break points as -0.634 and -2.366.

4. (b) 

Steady-State Error of a System with a Step-Function Input
Type 0; ess = R/(1 + Kp)
Type 1; ess = 0

Steady-State Error of A System with Ramp-Function Input
Type 0; ess = ∞
Type 1; ess = R/Kv
Type 2 or higher; ess = 0

5. (d)

6. (d)
\frac{{dL}}{{d\theta }} = (0 + 5 - 2\theta )x{10^{ - 6}} = (5 - 2\theta )x{10^{ - 6}}H/rad
For 5 A current
{T_d} = 12x{10^{ - 6}}\theta N - m
Also
{T_d} = \frac{1}{2}{I^2}.\frac{{dL}}{{d\theta }}
Equating
12x{10^{ - 6}}\theta = \frac{1}{2}x{5^2}x(5 - 2\theta )x{10^{ - 6}}
\Rightarrow \theta = 1.689rad = 1.689x{57.3^0} = {96.7^0}

7. (a) A rating of 30 kV is the minimum breakdown voltage at which transformer oil can be safely used in a power transformer.

8. (b) The sensitivity of the potentiometer is defined as the smallest potential difference that is measured by using a potentiometer. The sensitivity of the potentiometer can be increased by decreasing the potential gradient. i.e., by increasing the length of the potentiometer wire.

The sensitivity of the potentiometer can be increased by:
  • Increasing the length of the potentiometer wire
  • By reducing the current in the circuit by using a rheostat
9. (b) A galvanometer can be converted into a voltmeter by connecting it with a resistance in series so as to increase the overall resistance. A galvanometer can be converted into an ammeter by connecting it with a resistance in parallel which decreases the overall resistance.

10. (a) 
L = V/(dI/dt)
[L] = \frac{{M{L^2}{T^{ - 3}}{I^{ - 1}}}}{{I{T^{ - 1}}}}
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