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,
\[{{E}_{1}}=\dfrac{{{l}_{1}}}{L}V\] …………….. (2)
Similarly, when second battery is connected, the emf is given by,
\[{{E}_{2}}=\dfrac{{{l}_{2}}}{L}V\] ………… (1)
Therefore, from (1) and (2) we get,
\[\dfrac{{{E}_{1}}}{{{E}_{2}}}=\dfrac{{{l}_{1}}}{{{l}_{2}}}\].
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
\[R=290+10=300\Omega \]
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,
\[R=240\times \left( \dfrac{10}{400} \right)\]
\[R=6\Omega \] …………………. (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.