JEE Advanced 2016 · Paper 2, Physics question 10

Let one galvanometer carry its full-scale current $I_g$.

Voltage range.

• (A) All in series: $V=I_g(2R_C+2R)$.
• (B) G‖G in series with $2R$: the pair carries $2I_g$, so $V=2I_g\left(\frac{R_C}2+2R\right)=I_g(R_C+4R)$.

(B) exceeds (A) when $2R>R_C$, which holds. So (B) is true and (A) is false.

Current range.

• (C) All in parallel: the voltage is $I_gR_C$, so $I=2I_g+\dfrac{2I_gR_C}R$.
• (D) G-G in series, in parallel with $R\|R$: $I=I_g+\dfrac{2I_gR_C}{R/2}=I_g+\dfrac{4I_gR_C}R$.

(C) − (D) $=I_g\left(1-\dfrac{2R_C}R\right)>0$ for $R_C<R/2$. So (C) is true and (D) is false.

(B), (C)