Question

A potentiometer has a driving cell of negligible internal resistance. The balancing length of a Daniel cell is $5m$. If the driving cell had internal resistance, the balancing length of the same Denial cell would have been

• A. more
• B. less
• C. same
• D. cannot be said from the data

Answer 1

The correct option is A more

Let resistance of $AB=R$ and power supply has voltage $=V$, $AB=L$ and $AC=5m$

Current in the circuit $I=\frac{V}{R}$

So balancing voltage $V_{Bal}=R_{AC}\times I=(R\times \frac{5}{L})\times \frac{V}{R}=\frac{5V}{L}$ .... (1)

Now consider internal resistance of power supply $=r$ and balancing length $=l$

Current in the circuit $I_1=\frac{V}{R+r}$

Now balancing voltage $V_{Bal}=(R\times \frac{l}{L})\times \frac{V}{R+r}$ ........(2)

By equation (1)&(2) - $\frac{5V}{L}=(R\times \frac{l}{L})\times \frac{V}{R+r}⟹l=5(1+\frac{r}{R})⟹l>5m$