Potentiometer — Prelims Questions

A potentiometer wire of length $L$ and resistance $R$ is connected in series with a battery of EMF $E_0$ and internal resistance $r_0$. An unknown EMF $E_x$ is balanced at a length $l$ of the potentiometer wire. If the internal resistance of the unknown cell is $r_x$, what is the expression for $E_x$?

Two cells of EMFs $E_1$ and $E_2$ ($E_1 > E_2$) are connected in series to a potentiometer. When they are connected to assist each other, the balancing length is $l_1$. When they are connected to oppose each other, the balancing length is $l_2$. What is the ratio $E_1/E_2$?

A cell of EMF $1.5,\text{V}$ gives a balance point at $30,\text{cm}$ length of a potentiometer wire. If the cell is shunted by a resistance of $5,Omega$, the balance point shifts to $25,\text{cm}$. The internal resistance of the cell is:

Which of the following conditions is NOT essential for a potentiometer to work accurately?

To increase the sensitivity of a potentiometer, which of the following actions would be most effective?

A potentiometer wire of length $10,\text{m}$ has a resistance of $15,Omega$. It is connected in series with a $2,\text{V}$ battery and an external resistance of $5,Omega$. An unknown cell balances at $6,\text{m}$ length of the wire. What is the EMF of the unknown cell?