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

Answer: (D)

$3.75 \times 10^{- 3}\; Ω$

Answer 2

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 : $3.75 \times 10^{-3} \, \Omega$