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 address this issue, we must ascertain the resistance value of the shunt resistor (\(R_s\)) that enables the galvanometer to register a current of 8 A, given that its full-scale deflection current is limited to 3 mA. This necessitates an understanding of how shunt resistance functions in parallel with a galvanometer.

The galvanometer achieves full-scale deflection at a current designated as \(I_g\), which is provided as 3 mA, equivalent to \(3 \times 10^{-3} \, \text{A}\). The aggregate current (\(I\)) to be measured is 8 A.

A shunt resistance (\(R_s\)) is employed to divert the majority of the current, allowing only a minimal portion to traverse the galvanometer. The current flowing through the shunt is calculated as \(I_s = I - I_g\).

The relationship governing the galvanometer, shunt resistance, and the total current is articulated as:

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

In this equation:

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

Applying the aforementioned relationship:

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

Upon substituting the known values:

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

This simplifies to:

\(0.03 = 7.997 \times R_s\)

Consequently, the shunt resistance is:

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

Therefore, the shunt resistance required for measuring a current of 8 A is \(3.75 \times 10^{-3} \, \Omega\), aligning with the correct selection.