Question

Calculate the value of the unknown potential V for the given potentiometer circuit. The total length (400 cm) of the potentiometer wire has a resistance of 10Ω and the balance point is obtained at a length of 240 cm

A. 0.06 V
B. 0.6 V
C. 6 V
D. None of these

Answer 1

Hint: In this question we have been asked to calculate the unknown potential V for the given potentiometer circuit. Therefore, to solve this question, we shall first discuss what is a potentiometer briefly. We know that for a balanced point in a potentiometer, the ratio of two emf of a battery is equal to the ratio of lengths. Therefore, we shall use this concept to calculate the unknown potential or emf of the battery.
Formula used: $$V=IR$$

Complete step by step solution:
We know that potentiometer is the electrical device used to compare the emfs of two cells. It is also used to calculate the internal resistance of a cell or measure its potential difference. The balance point is obtained in a potentiometer by connecting one of the batteries between the galvanometer. The jockey is moved until the galvanometer shows no deflection. The length of wire is taken as $$l_1$$.
The emf of battery is then given as,
$$E_1={\displaystyle \frac{l_1}{L}}V$$ …………….. (2)
Similarly, when second battery is connected, the emf is given by,
$$E_2={\displaystyle \frac{l_2}{L}}V$$ ………… (1)
Therefore, from (1) and (2) we get,
$${\displaystyle \frac{E_1}{E_2}}={\displaystyle \frac{l_1}{l_2}}$$.
Now, from the diagram, we know that the resistance given is 290 ohms. This resistor is in series with the wire having 10 ohms resistance. Therefore, the total resistance is
$$R=290+10=300\mathrm{\Omega }$$
Therefore, using Ohm's law
We get,
$$V=IR$$
Substituting the given values
We get,
$$3=300\times I$$
Therefore,
$$I={10}^{-2}A$$ …………… (3)
 Now, it is also given that the resistance of 400 cm of wire is 10 ohms.
Therefore, resistance of 240 cm length of wire will be,
$$R=240\times \left({\displaystyle \frac{10}{400}}\right)$$
$$R=6\mathrm{\Omega }$$ …………………. (4)
Now, substituting (3) and (4) in Ohm's law
We get,
$$V_0={10}^{-2}\times 6$$
Therefore,
$$V_0=0.06V$$
Therefore, the correct answer is option A.

Note: A potentiometer is an electrical device with three-terminal resistors with sliding contact that forms an adjustable voltage divider. The potentiometer acts as the rheostat when only two terminals are used. It is a measuring device used to measure the electric potential of the circuit. Potentiometers are commonly used to control electrical devices such as audio control.