Question

The deflection in a moving coil galvanometer falls from 25 divisions to 5 divisions when a shunt of \( 24 \, \Omega \) is applied. The resistance of the galvanometer coil will be:

• A. \( 12 \, \Omega \)
• B. \( 96 \, \Omega \)
• C. \( 48 \, \Omega \)
• D. \( 100 \, \Omega \)

Answer 1

The Correct Option is B

To determine the resistance of a moving coil galvanometer, the concept of shunt resistance is employed. A shunt is implemented to reduce the galvanometer's deflection. The deflection of a galvanometer is directly proportional to the current flowing through it, and inversely proportional to the applied shunt resistance.

Given:

• Initial deflection, \( D_1 = 25 \) divisions
• Final deflection, \( D_2 = 5 \) divisions
• Shunt resistance, \( S = 24 \, \Omega \)

The relationship between deflections and resistances is expressed by the formula:

\(\frac{D_1}{D_2} = 1 + \frac{G}{S}\)

where \( G \) represents the resistance of the galvanometer coil.

Substituting the provided values:

\(\frac{25}{5} = 1 + \frac{G}{24}\)

Simplifying the left side of the equation yields:

\(\frac{25}{5} = 5\)

Therefore:

\(5 = 1 + \frac{G}{24}\)

Rearranging to solve for the term with \( G \):

\(5 - 1 = \frac{G}{24}\) \(4 = \frac{G}{24}\)

Finally, calculating \( G \):

\(G = 4 \times 24 = 96 \, \Omega\)

The resistance of the galvanometer coil, \( G \), is \( 96 \, \Omega \).

The determined resistance of the galvanometer is \( 96 \, \Omega \).