Question

A galvanometer having a resistance of 4 \( \Omega \) is shunted by a wire of resistance 2 \( \Omega \). If the total current is 1.5 A, the current passing through the shunt is

• A. 1.25 A
• B. 1 A
• C. 0.75 A
• D. 0.5 A

Hint:

To solve for currents in parallel circuits, use the ratio of the resistances to find the proportion of current passing through each resistor.

Answer 1

The Correct Option is B

In a parallel combination, the total current \( I \) is the sum of the current through the galvanometer \( I_g \) and the current through the shunt \( I_s \). The total current is 1.5 A, and the resistance of the galvanometer is \( 4 \, \Omega \), while the resistance of the shunt is \( 2 \, \Omega \). Using the formula for parallel resistances and currents, we can determine the current through the shunt: \[ \frac{I_g}{I_s} = \frac{R_s}{R_g} \quad \text{where } R_s = 2 \, \Omega \text{ and } R_g = 4 \, \Omega \] \[ \frac{I_g}{I_s} = \frac{2}{4} = \frac{1}{2} \] Thus, the current through the shunt is 1 A. So, the correct answer is (B).