Question

There is a galvanometer of resistance $100\Omega$ and full scale current $I_g = 1$ mA. Find shunt resistance required to increase its range to $5$ mA.

• A. $25\Omega$
• B. $0.25\Omega$
• C. $0.5\Omega$
• D. $1\Omega$

Hint:

Shunt resistance is always much smaller than galvanometer resistance.

Answer 1

The Correct Option is A

Step 1: Understand the purpose of the shunt

To extend the current range of a galvanometer, a low resistance called a shunt is connected in parallel with it so that most of the current bypasses the galvanometer.

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Step 2: Write the formula for shunt resistance

The shunt resistance R_s is given by:

R_s = (R_g · I_g) / (I − I_g)

where
R_g = resistance of galvanometer
I_g = full-scale deflection current of galvanometer
I = desired maximum current

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Step 3: Substitute the given values

R_g = 100 Ω
I_g = 1 mA = 0.001 A
I = 5 mA = 0.005 A

R_s = (100 × 0.001) / (0.005 − 0.001)

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Step 4: Perform the calculation

R_s = 0.1 / 0.004

R_s = 25 Ω

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Final Answer:

The shunt resistance required is
25 Ω