This set of Electrical Measurements written test Questions & Answers focuses on “Advanced Problems on Indicating Instruments – 2”.

1. A current of – 8 + 6\(\sqrt{2}\) (sin (ωt + 30°)) A is passed through three meters. The respective readings (in ampere) will be?

a) 8, 6 and 10

b) 8, 6 and 8

c) – 8, 10 and 10

d) -8, 2 and 2

View Answer

Explanation: PMMC instrument reads only DC value and since it is a centre zero type, so it will give – 8 values.

So, rms = \(\sqrt{8^2 +(\frac{6\sqrt{2}}{\sqrt{2}})^2}\) = 10 A

Moving iron also reads rms value, so its reading will also be 10 A.

2. A rectifier type AC voltmeter consists of a series resistance R, an ideal full-wave rectifier bridge and a PMMC instrument. The internal resistance of the instrument is 100 Ω and a full- scale deflection is produced by a DC current of 1 mA. A voltage of 100 V (rms) is applied to the input terminals. The value of R required is?

a) 63.56 Ω

b) 89.83 Ω

c) 89.83 kΩ

d) 141.3 kΩ

View Answer

Explanation: V

_{OAverage}= 0.636 × \(\sqrt{2}\) V

_{rms}= 0.8993 V

_{rms}

The deflection with AC is 0.8993 times that with DC for the same value of voltage V

S

_{AC}= 0.8993 S

_{DC}

S

_{DC}of a rectifier type instrument is \(\frac{1}{I_{fs}}\) where I

_{fs}is the current required to produce full scale deflection, I

_{fs}= 1 mA; R

_{m}= 100 Ω; S

_{DC}= 10

^{3}Ω/V

S

_{AC}= 0.8993 × 1000 = 899.3 Ω/V. Resistance of multiplier R

_{S}= S

_{AC}V – R

_{m}– 2R

_{d}, where R

_{d}is the resistance of diode, for ideal diode R

_{d}= 0

∴ R

_{S}= 899.3 × 100 – 100 = 89.83 kΩ.

3. A current of [2 + \(\sqrt{2}\) sin (314t + 30) + 2\(\sqrt{2}\) cos (952t +45)] is measured with a thermocouple type, 5A full scale, class 1 meter. The meter reading would lie in the range?

a) 5 A ± 1 %

b) (2 + 3\(\sqrt{2}\)) A ± 1%

c) 3 A ± 1.7 %

d) 2 A ± 2.5 %

View Answer

Explanation: I = [2 + \(\sqrt{2}\) sin (314t +30°) + 2\(\sqrt{2}\) cos (952t + 45°)] Thermocouple measure the rms value of current.

\(I_{rms} = [2^2 + (\frac{\sqrt{2}}{\sqrt{2}})^2 + (\frac{2\sqrt{2}}{\sqrt{2}})^2]^{1/2} = \sqrt{9}\) = 3 A ± 1.7%.

4. A 50 Hz voltage is measured with a moving iron voltmeter and a rectifier type AC voltmeter connected in parallel. If the meter readings are V_{a} and V_{b} respectively. Then the form factor may be estimated as?

a) \(\frac{V_a}{V_b}\)

b) \(\frac{1.11 V_a}{V_b}\)

c) \(\frac{\sqrt{2} V_a}{V_b}\)

d) \(\frac{π V_a}{V_b}\)

View Answer

Explanation: Form factor of the wave = \(\frac{RMS value}{Mean value}\)

Moving iron instrument will show rms value. Rectifier voltmeter is calibrated to read rms value of the sinusoidal voltage that is, with form factor of 1.11.

∴ Mean value of the applied voltage = \(\frac{V_b}{1.11}\)

∴ Form factor = \(\frac{V_a}{V_b/1.11} = \frac{1.11 V_a}{V_b}\)

5. A moving iron ammeter produces a full-scale torque of 240 μN-m with a deflection of 120° at a current of 10 A. the rate of change of self-inductance (μH/rad) of the instrument at full scale is?

a) 2.0 μH/rad

b) 4.8 μH/rad

c) 12.0 μH/rad

d) 114.6 μH/rad

View Answer

Explanation: At full scale position, \(\frac{1}{2} I^2 \frac{dL}{dθ}\) = T

_{C}

\(\frac{1}{2} 10^2 \frac{dL}{dθ}\) = 240 × 10

^{-6}

∴ \(\frac{dL}{dθ}\) = 4.8 μH/rad.

6. A moving coil of a meter has 250 turns and a length and depth of 40 mm and 30 mm respectively. It is positioned in a uniform radial flux density of 450 mT. The coil carries a current of 160 mA. The torque on the coil is?

a) 0.0216 N-m

b) 0.0456 N-m

c) 0.1448 N-m

d) 1 N-m

View Answer

Explanation: Given, N = 250, L = 40 × 10

^{-3}, d = 30 × 10

^{-3}m, I = 160 × 10

^{-3}A, B = 450 × 10

^{-3}T

Torque = 250 × 450 × 10

^{-3}× 40 × 10

^{-3}× 30 × 10

^{-3}× 160 × 10

^{-3}= 200 × 10

^{-6}N-m = 0.0216 N-m.

7. Two 100 μA full-scale PMMC meters are employed to construct a 10 V and a 100 V full-scale voltmeter. These meters will have figure of merit (sensitivities) as?

a) 10 kΩ/V and 10 kΩ/V

b) 100 kΩ/V and 10 kΩ/V

c) 10 kΩ/V and 100 kΩ/V

d) 10 kΩ/V and 1 kΩ/V

View Answer

Explanation: \(S_V = \frac{1}{I_{SS}}\) = current required for full scale deflection

\(S_V = \frac{1}{100 × 10^{-6}}\) = 10 kΩ/V.

8. A PMMC rated as 100 μA is used in a rectifier type of instrument which uses full wave rectification. What is the sensitivity on sinusoidal AC?

a) 4.5 kΩ/V

b) 18 kΩ/V

c) 10 kΩ/V

d) 9 kΩ/V

View Answer

Explanation: Sensitivity = \(\frac{1}{100 × 10^{-6}}\) = 10 kΩ/V

For full-wave rectification S

_{AC}= 0.9 + S

_{DC}= 0.9 × 10 = 9kΩ/V.

9. The discharge of a capacitor through a ballistic galvanometer produces a damped frequency of 0.125 Hz and successive swings of 120, 96 and 76.8 mm. The damping ratio is?

a) 0.0568

b) 0.0887

c) 0.0357

d) 0.0441

View Answer

Explanation: Logarithmic decrement, δ = \(ln \frac{x_1}{x_2} = ln \frac{120}{96}\) = 0.225

Now, δ is related to damping ratio K as, K = \(\frac{1}{(1 + (\frac{2π}{δ})^2)^{0.5}}\)

K = \(\frac{1}{(1 + (\frac{2π}{0.225})^2)^{0.5}}\)

∴ K = 0.0357.

10. The discharge of a capacitor through a ballistic galvanometer produces a damped frequency of 0.125 Hz and successive swings of 120, 96 and 76.8 mm. The logarithmic decrement is?

a) 0.225

b) 0.565

c) 0.484

d) 0.7887

View Answer

Explanation: Logarithmic decrement, δ = \(ln \frac{x_1}{x_2} = ln \frac{120}{96}\) = 0.225

Now, δ is related to damping ratio K as, K = \(\frac{1}{(1 + (\frac{2π}{δ})^2)^{0.5}}\)

K = \(\frac{1}{(1 + (\frac{2π}{0.225})^2)^{0.5}}\)

∴ K = 0.0357.

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