Question

A galvanometer having coil resistance 10 Ω shows a full scale deflection for a current of 3 mA. For it to measure a current of 8 A, the value of the shunt should be:

• A. \(10^{- 3}\; Ω\)
• B. \(7.5 \times 10^{- 3}\; Ω\)
• C. \(6.75 \times 10^{- 3}\; Ω\)
• D. \(3.75 \times 10^{- 3}\; Ω\)

Answer 1

The Correct Option is D

Step 1: Given Data: - Galvanometer resistance \( G = 10 \Omega \) - Full-scale deflection current \( I_g = 3 \, \text{mA} = 3 \times 10^{-3} \, \text{A} \) - Desired current to be measured \( I = 8 \, \text{A} \)

Step 2: Calculate the Shunt Resistance \( S \): - In order to convert the galvanometer into an ammeter, the shunt resistance \( S \) is given by:

\[ S = \frac{I_g \, G}{I - I_g} \]

Step 3: Substitute the Values:

\[ S = \frac{(3 \times 10^{-3}) \times 10}{8 - 0.003} \\ S = \frac{0.03}{7.997} \approx 3.75 \times 10^{-3} \, \Omega \]

So, the correct answer is : \( 3.75 \times 10^{-3} \, \Omega \)