Question

Consider two identical galvanometers and two identical resistors with resistance $R$. If the internal resistance of the galvanometers $R_C<R/2$, which of the following statement(s) about any one of the galvanometers is(are) true?

• A. The maximum voltage range is obtained when all the components are connected in series
• B. The maximum voltage range is obtained when the two resistors and one galvanometer are connected in series, and the second galvanometer is connected in parallel to the first galvanometer
• C. The maximum current range is obtained when all the components are connected in parallel
• D. The maximum current range is obtained when the two galvanometers are connected in series and the combination is connected in parallel with both the resistors

Answer 1

Answer: (A), (C)

$V_{\max }=2I_{gmax}\left(2R+\frac{R_C}{2}\right)$
$V_{\max }=I_{gmax}\left(4R+R_C\right)$

$I_{g\max }{R}_c=\left(I_{\max }-2I_{g\max }\right)\frac{R}{2}$
$I_{g\max }{R}_c=\left(I_{\max }\frac{R}{2}-I_{g\max }R\right)$
$I_{g\max }\left(R_c+R\right)=I_{\max }\frac{R}{2}$
$I_{\max }=I_{g\max }\times \frac{\left(R_C+R\right)}{R/2}$

$I_{\max }=I_{g\max }\left(\frac{2R_C+\frac{R}{2}}{\frac{R}{2}}\right)$