Heating Effect of Current and Electrical Measuring Instruments | Physics JEE previous year questions with Solutions

Q 11 :
Two resistance of 100 $Ω$ and 200 $Ω$ are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across $100 Ω$ resistance, which gives reading as 1V. The resistance of voltmeter must be ________ $Ω$ . [2024]

0%

(200)

Given potential across Voltmeter = 1V

$∴ Current in 100 Ω = \frac{1}{100} A = i_{1}$

$200 Ω = \frac{3}{100} A \Rightarrow$ as total potential $= 4 V_{1} & 1 V$ is drop across $100 Ω$

Let current in voltmeter = i

$i_{1} + i_{2} = i_{0}$

$i_{2} + \frac{1}{100} = \frac{3}{200}$

$i_{2} + \frac{3}{200} - \frac{1}{100} = \frac{1}{200} A_{1}$

$V = I R_{1} \Rightarrow 1 = \frac{1}{200} (r), \Rightarrow r = 200 Ω$

Q 12 :
Consider a moving coil galvanometer (MCG):

A. The torsional constant in moving coil galvanometer has dimensions [ ${ML}^{2} T^{- 1}$ ]

B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.

C. If we increase number of turns (N) to its double (2N), then the oltage sensitivity doubles.

D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.

E. Current sensitivity of MCG depends inversely on number of turns of coil.

Choose the correct answer from the options given below: [2025]

A, B only
A, D only
B, D, E only
A, B, E only

1

2

3

4

(1)

(A) $τ = C θ \Rightarrow [{ML}^{2} T^{- 2}] = [C] [1]$

(B) $C . S . = \frac{θ}{I} = \frac{BNA}{C};$

$V . S . = \frac{BNA}{RC}$ [R = also depends on 'N']

(C) $V . S . \infty \frac{NAB}{CR} R \to NR$

(D) Shunt of law of resistance, False [Theory]

(E) E [False] C.S $\infty$ N

$\Rightarrow C . S = \frac{NAB}{C}$

Q 13 :
A galvanometer having a coil of resistance 30 $Ω$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X} Ω$ , where X is [2025]

447
298
149
596

1

2

3

4

(3)

Figure

$I_{g} R_{g} = (I - I_{g}) r_{s}$

$20 \times 10^{- 3} \times 30 = (3 - 0.02) \times r_{s}$

$r_{s} = (\frac{0.6}{2.98}) = \frac{30}{x}$

$x = (\frac{2.98 \times 30}{0.6}) = 149$

Q 14 :
In a moving coil galvanometer, two moving coils $M_{1}$ and $M_{2}$ have the following particulars:

$R_{1} = 5 Ω, N_{1} = 15, A_{1} = 3.6 \times 10^{- 3} m^{2}, B_{1} = 0.25 T$

$R_{2} = 7 Ω, N_{2} = 21, A_{2} = 1.8 \times 10^{- 3} m^{2}, B_{2} = 0.50 T$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_{1}$ and $M_{2}$ ? [2025]

1 : 1
1 : 4
1 : 3
1 : 2

1

2

3

4

(1)

$K θ = N I A B \Rightarrow \frac{θ}{I} = \frac{N A B}{K}$

Voltage sensitivity $= \frac{θ}{V} = \frac{θ}{R I} = \frac{N A B}{K R}$

Ratio of voltage sensitivity $= (\frac{N_{1} A_{1} B_{1}}{R_{1}}) (\frac{R_{2}}{N_{2} A_{2} B_{2}})$

Ratio $= (\frac{N_{1} A_{1} B_{1}}{N_{2} A_{2} B_{2}}) \frac{R_{2}}{R_{1}} = \frac{15 \times 3.6 \times 0.25}{21 \times 1.8 \times 0.5} \times \frac{7}{5} = \frac{1}{1}$

Topic Question Set

Q 11 :
Two resistance of 100 $Ω$ and 200 $Ω$ are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across $100 Ω$ resistance, which gives reading as 1V. The resistance of voltmeter must be ________ $Ω$ . [2024]

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Q 13 :
A galvanometer having a coil of resistance 30 $Ω$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X} Ω$ , where X is [2025]

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Topic Question Set

Q 11 : Two resistance of 100Ω and 200Ω are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across 100Ω resistance, which gives reading as 1V. The resistance of voltmeter must be ________ Ω. [2024]

0%

Q 13 : A galvanometer having a coil of resistance 30 Ω need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be 30XΩ, where X is [2025]

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Q 11 :
Two resistance of 100 $Ω$ and 200 $Ω$ are connected in series with a battery of 4V and negligible internal resistance. A voltmeter is used to measure voltage across $100 Ω$ resistance, which gives reading as 1V. The resistance of voltmeter must be ________ $Ω$ . [2024]

Q 13 :
A galvanometer having a coil of resistance 30 $Ω$ need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $\frac{30}{X} Ω$ , where X is [2025]