Explanation:

A shunt is a parallel resistor that is connected to the galvanometer for measuring larger currents. It is used to divert a portion of the current away from the galvanometer, allowing only a fraction of the current to pass through the galvanometer. The deflection in a moving coil galvanometer is directly proportional to the current flowing through it. The deflection can be reduced by connecting a shunt resistor in parallel with the galvanometer.

Given, the deflection falls from 50 divisions to 10 divisions when a shunt of 12 ohm is applied.

Let the resistance of the galvanometer be Rg and the current passing through it be Ig. The current passing through the shunt resistor is Is = (50-10)/12 = 3.33Ig.

Solution:

Using Kirchhoff's current law, the total current passing through the circuit is given by:

I = Ig + Is

I = Ig + 3.33Ig

I = 4.33Ig

The potential difference across the galvanometer is given by:

Vg = IgRg

The potential difference across the shunt resistor is given by:

Vs = IsRs

Since the two resistors are connected in parallel, they have the same potential difference. Therefore,

Vg = Vs

IgRg = 3.33IgRs

Rg = 3.33Rs

Using the given value of the shunt resistor, Rs = 12 ohm, we can find the resistance of the galvanometer as:

Rg = 3.33 x 12

Rg = 39.96 ohm

Therefore, the resistance of the galvanometer is 39.96 ohm.

S=G/n-1