1. Principle of the shunt method

To determine the resistance $G$ of a galvanometer, a shunt resistance $S$ is connected in parallel with it.

If the initial deflection is proportional to current through the galvanometer, then:

• Let the current through galvanometer initially be $I_g$ giving full observed deflection.
• After connecting shunt $S$, suppose the deflection becomes a fraction of the original.

Since deflection $\propto$ current through galvanometer, if the deflection becomes $\dfrac{1}{3}$ of the original, then the new current through galvanometer is $I_g' = \frac{I_g}{3}.$

2. Current division in galvanometer and shunt

The galvanometer of resistance $G$ and shunt $S$ are in parallel, so potential difference across both is same: $I_g' G = I_s S$ where $I_s$ is current through shunt.

Also, total current entering the parallel combination is the same as before in this standard method, so $I_g = I_g' + I_s.$

Using $I_g' = \dfrac{I_g}{3}$, $I_s = I_g - I_g' = I_g - \frac{I_g}{3} = \frac{2I_g}{3}.$

Now apply equal potential condition: $I_g' G = I_s S$ $\frac{I_g}{3}G = \frac{2I_g}{3}S$ Cancel $\dfrac{I_g}{3}$: $G = 2S.$

3. Conclusion

Thus, in the $\dfrac{1}{3}$ deflection method, $\boxed{G = 2S}$ so the galvanometer resistance is twice the shunt resistance.

4. Option check

• A: False
• B: True, because $G=2S$
• C: False
• D: False

Hence the correct option is $\boxed{\text{B}}$