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

To solve this problem, we need to determine the value of the shunt resistor (\(R_s\)) that allows the galvanometer to measure a current of 8 A when the full-scale deflection current is only 3 mA. This involves understanding the concept of shunt resistance in parallel with a galvanometer.

The galvanometer shows a full-scale deflection at a current denoted as \(I_g\), which is given as 3 mA or \(3 \times 10^{-3} \, \text{A}\). The total current \(I\) that needs to be measured is 8 A. 

The shunt resistance (\(R_s\)) is used to bypass the majority of the current such that only a small portion passes through the galvanometer. The current through the shunt is given by \(I_s = I - I_g\).

The relation between the galvanometer, shunt resistance, and the total current is given by:

\(V_g = I_g \cdot R_g = I_s \cdot R_s\)

Where:

• \(V_g\) is the voltage across the galvanometer and the shunt (both in parallel)
• \(R_g\) is the resistance of the galvanometer coil, given as 10 Ω
• \(I_s = I - I_g = 8 - 0.003 = 7.997\) A

Using the above relation:

\(I_g \cdot R_g = I_s \cdot R_s\)

Substituting the values:

\(3 \times 10^{-3} \times 10 = 7.997 \times R_s\)

Simplifying gives:

\(0.03 = 7.997 \times R_s\)

Thus, the shunt resistance is:

\(R_s = \frac{0.03}{7.997} \approx 3.75 \times 10^{-3} \, \Omega\)

Therefore, the value of the shunt resistance required to measure a current of 8 A is \(3.75 \times 10^{-3} \, \Omega\), which corresponds to the correct option.

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