Question

A potentiometer has a uniform wire of length 5m. A battery of emf 10V and negligible internal resistance is connected between its ends. A secondary cell connected to the circuit gives balancing length at 200cm. The emf of the secondary cell is

• A. 4V
• B. 6V
• C. 2V
• D. 8V

Answer 1

The Correct Option is A

The potentiometer works on the principle that the potential difference across a uniform wire is directly proportional to the length of the wire. The formula to calculate the emf of the secondary cell is: \[ \frac{E_{\text{sec}}}{E_{\text{battery}}} = \frac{l_{\text{bal}}}{L} \] Where: - \(E_{\text{sec}}\) is the emf of the secondary cell. - \(E_{\text{battery}} = 10 \, \text{V}\) is the emf of the primary battery. - \(l_{\text{bal}} = 200 \, \text{cm} = 2 \, \text{m}\) is the balancing length. - \(L = 5 \, \text{m}\) is the total length of the potentiometer wire. Substituting the values into the formula: \[ \frac{E_{\text{sec}}}{10} = \frac{2}{5} \] Solving for \(E_{\text{sec}}\): \[ E_{\text{sec}} = 10 \times \frac{2}{5} = 4 \, \text{V} \] Thus, the emf of the secondary cell is 4 V. Therefore, the correct answer is (A) 4 V.

Answer 2

In the potentiometer experiment, the potential difference across the wire is constant, and the potential difference per unit length is uniform. The balancing length is the length of the wire required to balance the emf of the secondary cell. Let the total length of the wire be \( L = 5 \, \text{m} = 500 \, \text{cm} \), and the emf of the primary battery (10 V) is connected across the full length of the wire. The potential difference across the wire is: \[ V_{\text{wire}} = 10 \, \text{V} \] Now, the potential difference per unit length is: \[ \frac{V_{\text{wire}}}{L} = \frac{10}{500} = 0.02 \, \text{V/cm} \] For the secondary cell, the balancing length is 200 cm. So, the potential difference corresponding to this length is: \[ V_{\text{secondary}} = 0.02 \times 200 = 4 \, \text{V} \] Thus, the emf of the secondary cell is 4 V.

Therefore, the correct answer is (A) 4 V.