Question

In the given circuit, the terminal potential difference of the cell is :

• A. 2 V
• B. 4 V
• C. 1.5 V
• D. 3 V

Answer 1

The Correct Option is A

The circuit has a 3 V cell connected to resistances of \(1 \, \Omega\), \(4 \, \Omega\), and \(4 \, \Omega\). The total resistance \(R_{\text{total}}\) of the circuit is calculated as:
\[ R_{\text{total}} = R_{\text{internal}} + R_{\text{external}} \]
The external resistance is a parallel combination of \(4 \, \Omega\) and \(4 \, \Omega\):
\[ R_{\text{parallel}} = \frac{1}{4} + \frac{1}{4} = 2 \, \Omega. \]
Thus, the total resistance becomes:
\[ R_{\text{total}} = 1 \, \Omega + 2 \, \Omega = 3 \, \Omega. \]
The current in the circuit is:
\[ i = \frac{\text{EMF}}{R_{\text{total}}} = \frac{3 \, \text{V}}{3 \, \Omega} = 1 \, \text{A}. \]
The terminal potential difference \(V_{\text{terminal}}\) is given by:
\[ V_{\text{terminal}} = \text{EMF} - i R_{\text{internal}} = 3 \, \text{V} - (1 \, \text{A} \cdot 1 \, \Omega) = 2 \, \text{V}. \]
Final Answer: 2 V