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

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Current Electricity

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of

24Ω

is applied. The resistance of galvanometer coil will be :

Answer: (B)

Let

k

be the galvanometer's current-per-division constant, so with no shunt the same total current

I = 25 k

produces full 25-division deflection.

With shunt

S = 24 Ω

applied, the same total current

I = 25 k

splits between

G

and

S

; the deflection now corresponds to a galvanometer current of

5 k

. By the current-divider rule:

5 k = 25 k \cdot \frac{S}{G + S} ⟹ \frac{1}{5} = \frac{24}{G + 24} ⟹ G + 24 = 120 ⟹ G = 96 Ω

Key confirmed: B.

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Single correct option