A galvanometer has a current sensittivity of $1mA$ per division. A variable shunt is connected across the galvanometer and the combination is put in series with a resistance of $500\Omega$ and cell of internal resistance $1\Omega$. It gives deflection of $5$ division for shunt of $5$ ohm and $20$ division for shunt of $25$ ohm. the emf of cell is

The correct option is A $47.1V$
$R_g{I}_g=S(I-I_g)$

$⟹I=I_g(R_g+S)/S$

Case 1: $S=5\Omega ,I_g=5mA$

$⟹I_1=R_g+\mathrm{5.............}\left(i\right)$

Case 2: $S=25\Omega ,I_g=20mA$

$⟹I_2=0.8(R_g+25)=0.8R_g+\mathrm{20.............}\left(ii\right)$

$E=501I+I_g{R}_g................\left(iii\right)$

Substituting $\left(i\right)in\left(iii\right),$

$E=2505+506R_g.............\left(iv\right)$

Substituting $\left(ii\right)in\left(iii\right),$

$E=10020+420.8R_g.............\left(v\right)$

Solving $\left(iv\right)\&\left(v\right),$

$E=47136mV$

$E\approx 47.1V$