Question:

In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60 μA/division. In the absence of shunt resistance, the galvanometer produces a deflection of θ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of θ/2, is closest to 55 Ω, 110 Ω, 220 Ω, 550 Ω

110Ω

550Ω

55Ω

220Ω

(i) r is not there.
I = 9 × 60 μA = 540 × 10⁻⁶ A

V = IR
6 = 540 × 10⁻⁶ (11000 + G)

G = 11000/9 -1000 ≈ 11000/9

(ii) G = RS/(R - S)

11000/9 = 11000S/(11000 - S)
This gives S = 110