Question

Consider two identical galvanometers and two identical resistors with resistances $R$ each. If the internal resistance of the galvanometers$\left(R_c\right)$ is less than $R/2$, 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 galvanometers are connected in parallel and the combination is connected in series to the resistances.
• C. The maximum current range is obtained when all the components are connected in parallel
• D. The maximum current range is obtained when the galvanometers are connected in series and the two resistances are connected in parallel to the combination of the galvanometers.

Answer 1

Answer: (B), (C)

The correct options are
B The maximum voltage range is obtained when the two galvanometers are connected in parallel and the combination is connected in series to the resistances.
C The maximum current range is obtained when all the components are connected in parallel


When all the components are connected in series, voltage reading
$V_1=2i_g(R_c+R)$
Given $R>2R_c\Rightarrow R_c+R>3R_c$
$\Rightarrow V_1>6i_g{R}_c$
When the two galvanometers are connected in parallel and the combination is connected in series to the resistances.
Voltage reading,
$V_2=2i_g(\frac{R_c}{2}+2R)$
$V_2=i_g(R_c+4R)$
$R>2R_c\Rightarrow 4R+R_c\ge 9R_c$
$\Rightarrow V_2>9i_g{R}_c$
Hence $V_2>V_1$
When all the components are connected in parallel,
$i_g.R_c=iR\Rightarrow i=\frac{i_g{R}_c}{R}$
$i_1=2(i_g+i)$
$i_1=2(i_g+\frac{i_g{R}_c}{R})$
$i_1=2i_g(1+\frac{R_c}{R})$
When the galvanometers are connected in series and the two resistances are connected in parallel to the combination of the galvanometers,
$i_g\left(2R_c\right)=iR$
$\Rightarrow i=2i_g\left(\frac{R_c}{R}\right)$
$i_2=i_g+2i$
$i_2=i_g(1+\frac{4R_c}{R})$
Hence $i_1>i_2$