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QUESTION: 1

What is the voltage across the capacitor in the given figure 35s after the input voltage

steps from 0V to 54V, if the value of the resistor is 47 kΩ and the capacitor is 1.5F?

Solution:
E_{c} = 54(1 − e^{−35 × 1000000/1000 × 47 × 1000 × 1.5})V = 54 (1 − 1/e^{0.5})V

E_{c} = 54(1 − 0.606) = 21.3V

In an RC network when a step voltage is applied, the voltage across the capacitor is given by the equation

E_{c} = E{1− e^{-(t/RC)}}

where E_{c} is the voltage across the capacitor at any instant of time, E is the source

voltage, t is the time (seconds) after the step is applied, R is in ohms and C is in farads.

QUESTION: 2

What is the time constant for the circuit shown in the given figure, if the resistor has a

value of 220 kΩ, and the capacitor is 2.2 F?

Solution:
t = 2.2 × 10^{−6} × 220 × 10^{3} sec = 484 × 10^{−3} sec = 0.484 sec

The time constant of the voltage in a capacitive circuit is defined as:

t = CR

where t is the time (seconds) it takes for the voltage to reach 63.2% of its final or

aiming voltage after the application of an input voltage step (charging or discharging).

QUESTION: 3

The resistive elements in a strain gauge are each 5kΩ. A digital voltmeter with ranges of 10V, 1V, and 0.1V, and a resolution of 0.1% of FSD, is used to measure the output voltage. If R_{2} is the fixed element and R_{1} is the element measuring strain, what is the minimum change in R_{1} that can be detected? Assume a supply of 10V.

Solution:
To measure the output voltage ≈ 5V, the 10V range is required, giving a resolution or sensitivity of 10 mV.

V_{R} = 5.01V = 5,000 × 10/(R_{1} + 5,000)V

5.01(R_{1} + 5,000) = 50,000

R_{1} = (50,000/5.01) − 5,000 = 4,980Ω

Resolution = 5,000 − 4,980 = 20Ω

QUESTION: 4

Resistors R_{1 }and R_{2} in the bridge circuit shown in the given figure are the strain gauge elements of 5kΩ each. Resistors R_{3} and R_{4} are fixed resistors, with values of 4.3 kW. A digital voltmeter with ranges of 10V, 1V, and 0.1V, and a resolution of 0.1% of FSD, is used to measure the output voltage. What is the minimum change in R_{1} that can be detected by the meter? Assume the supply E is 10V.

Solution:
The voltage at point C will be 5.0V, because R_{3} = R_{4}, and the voltage at C equals one-half of the supply voltage. The voltmeter can use the 0.1V range, because the offset is 0V, giving a resolution of 0.1 mV. The voltage that can be sensed at A is given by

E_{AD} = 10 × R_{2}/(R_{1} + R_{2}) = 5.00 + 0.0001V

R_{1} = (50,000/50,001) − 5,000Ω

R_{1} = −49,999

Resolution = 1Ω

QUESTION: 5

If the bridge circuit in the given figure is balanced, with R_{1} = 15 kΩ, R_{2} = 27 kΩ, R_{3}= 18 kΩ, and C_{1} = 220 pF, what are the values of R_{4} and C_{2}?

Solution:
R_{2}R_{3} = R_{1}R_{4}

R_{4} = 27 × 18/15 = 32.4 kΩ

Additionally,

C_{2}R_{2} = C_{1}R_{1}

C_{2} = 220 × 15/27 = 122 pF

QUESTION: 6

In the potentiometer circuit shown in the figure, the expression for V_{x} is

Solution:

Using KVL,

V_{x} + (αR) 2V/R - V = 0

QUESTION: 7

The response of a first-order measurement system to a unit step input is 1 – e– 0.5t, where t is in seconds. A ramp of 0.1 units per second is given as the input to this system. The error in the measured value after transients have died down is

Solution:

QUESTION: 8

A metal wire has a uniform cross-section A, length, and resistance R between its two endpoints. It is uniformly stretched so that its length becomes l. The new resistance is

Solution:

Volume is constant

lA = l’A’

lA = α l A’

A’ = A/α

R’ = ρl'/A' = ρ αlα/A = α^{2 }R

QUESTION: 9

A variable air gap type capacitor consists of two parallel plates: a fixed plate and a moving plate at a distance x. If a potential V is applied across the two plates, then the force of attraction between the plates is related to x as

Solution:

E = ½ CV^{2.} = ½ ε*A*/x V^{2}

F = -δ*E*/δ*X* = ½ ε*A*/xx V^{2 } which is inversely proportional to x^{2}

QUESTION: 10

The expression for the capacitance (C in pF) of a parallel plate capacitor is given by:

C = 6.94 × 10^{– 3 }(d^{2}/S). The diameter (d) of each plate is 20 mm and the spacing between the plates

(S) is 0.25 mm. The displacement sensitivity of the capacitor is approximate:

Solution:

C = 6.94 x 10^{- 3} (d^{2}/S) PF

Displacement sensitivity = dC/dS = -6.94 x 10^{ - 3} x 20 ^{2} / (0.25)^{2} = - 44.4 pF/mm

QUESTION: 11

Which of the following can be measured using a Wheatstone bridge?

Solution:
Wheatstone bridge cannot be limited to measurement of a single quantity only, it can be used to measure resistance, capacitance, impedance, inductance etc. with some modifications.

QUESTION: 12

Accuracy in a bridge measurement depends on

Solution:
Both sensitivity of indicator and applied voltage affects the accuracy in bridge measurement.

QUESTION: 13

In a Wheatstone bridge, which of the following is used as a null detector?

Solution:
Null detector is used to indicate zero current flow, and the device used is a galvanometer.

QUESTION: 14

Which of the following statements is correct for impedance?

Solution:
Impedance of pure resistance is purely real and for an inductor purely imaginary, where the inductor is a reactive component.

QUESTION: 15

What is the purpose of Owens Bridge?

Solution:
Owens Bridge is an AC bridge that is used to measure reactance.

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