In a potentiometer experiment, it is found that no current passes through the galvanometer when the

Question

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by a resistance of $5 \Omega$, a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.\

Professor PC Thomas Classes · Answer

(b) : Without shunting condition: On balancing\ $\varepsilon_s=52 	imes k$ ...(i)\ where $k$ is potential gradient of wire.\ With shunting condition :\ On balancing 
$\varepsilon_s-\frac{\varepsilon_s}{(r+R)} r=40 	imes k$ ...(ii)\ From eqns. (i) and (ii),\ $\frac{1}{1-\frac{r}{r+R}}=\frac{52}{40} \Rightarrow \frac{r+R}{R}=\frac{52}{40}$\ $r=\left(\frac{52}{40} 	imes Right)-R=\left(\frac{52}{40} 	imes 5ight)-5$\ $	herefore \quad r=1.5 \Omega$