Question

\( I_g = 8\% \times I \). What is \( S \) (shunt) connected in terms of \( G \)?

• A. \( \frac{G}{11} \)
• B. \( \frac{2G}{23} \)
• C. \( \frac{3G}{25} \)
• D. \( \frac{4G}{29} \)

Hint:

The relationship \( S = \frac{I_g}{I_s} \cdot G \) is useful for calculating the shunt resistance, where \( I_g \) is the galvanometer current and \( I_s \) is the shunt current.

Answer 1

The Correct Option is B

The shunt resistance \( S \) is connected in parallel with the galvanometer resistance \( G \) to extend its range. The total current \( I \) is divided into two parts: \( I_g \): The current passing through the galvanometer. \( I_s \): The current passing through the shunt. From the given data: \[ I_g = 8\% \times I = 0.08I. \] Thus, the current through the shunt is: \[ I_s = I - I_g = I - 0.08I = 0.92I. \] Step 1: Use the relationship between \( S \) and \( G \).
The voltage across \( S \) is equal to the voltage across \( G \): \[ I_s \cdot S = I_g \cdot G. \] Substitute \( I_s = 0.92I \) and \( I_g = 0.08I \): \[ 0.92I \cdot S = 0.08I \cdot G. \] Simplify by canceling \( I \): \[ 0.92S = 0.08G. \] Solve for \( S \): \[ S = \frac{0.08G}{0.92}. \] Step 2: Simplify the fraction.
\[ S = \frac{8G}{92} = \frac{2G}{23}. \] Thus, the shunt resistance is: \[ S = \frac{2G}{23}. \]