JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Current Electricity

1. (A)$\frac{1}{3}$ deflection method cannot be used for determining the resistance of the galvanometer.
2. (B)$\frac{1}{3}$ deflection method can be used and in this case the G equals to twice the value of shunt resistance(s).✓ Correct
3. (C)$\frac{1}{3}$ deflection method can be used and in this case, the G equals to three times the value of shunt resistance(s)
4. (D)$\frac{1}{3}$ deflection method can be used and in this case the G value equals to the shunt resistance(s).

Answer: (B)

Solution

In the shunt method, the current divides between the galvanometer (resistance $G$) and the shunt (resistance $S$). The current ratio is:

$\frac{I_g}{I}=\frac{S}{S+G}$

For $\frac{1}{3}$ deflection, $I_g=\frac{I}{3}$:

$\frac{1}{3}=\frac{S}{S+G}$

Solving: $S+G=3S$, which gives $G=2S$.

Thus, the galvanometer resistance equals twice the shunt resistance.

JEE Main · 2022 · 25 Jun 2022 · Shift 1 · Single correct option