Question

In the circuit shown below, the potential difference between A and B is: graphics[width=0.5\linewidth]{Q1.png}

• A. 6 V
• B. 3 V
• C. 2 V
• D. 1 V

Hint:

For parallel cells with equal internal resistances: \[ E_{\text{eq}}=\frac{E_1+E_2+E_3+\cdots}{n} \]

Answer 1

The Correct Option is C

Step 1: Observe the arrangement of cells and resistors.
The three branches between points \(D\) and \(C\) are connected in parallel. Each branch contains: \[ 1\Omega \text{ resistor} \] and cells of emf: \[ 1V,\ 2V,\ 3V \]

Step 2: Find the equivalent emf between \(D\) and \(C\).
Since all resistances are equal, the equivalent emf is the average of the emfs: \[ E_{\text{eq}} = \frac{1+2+3}{3} \] \[ E_{\text{eq}} = \frac{6}{3} \] \[ E_{\text{eq}}=2V \]

Step 3: Determine the potential difference between A and B.
The outer resistors carry no current because the circuit is balanced. Hence, there is no voltage drop across them. Therefore: \[ V_{AB}=V_{DC} \] Thus: \[ V_{AB}=2V \]

Step 4: Identify the correct option.
Hence, the correct answer is: \[ \boxed{2V} \] Therefore: \[ \boxed{\mathrm{(C)}} \]