The potential difference between points A and B is:

The correct answer is Option (2) → \( \frac{10}{3} \) V

The two branches (2 Ω with 4 Ω, and 2 Ω with 1 Ω) are in parallel across the 10 V cell, so each has the full 10 V across it. The current in each branch follows from Ohm’s law, and the potential of A and of B is found by moving from the common left end through the first 2 Ω resistor of each branch.

    \( I_1 = \frac{10}{2+4} = \frac{5}{3}\,\mathrm{A} \) (upper branch)
    \( I_2 = \frac{10}{2+1} = \frac{10}{3}\,\mathrm{A} \) (lower branch)

Taking the common left end at 10 V and the common right end at 0 V:

    \( V_A = 10 - 2\times\frac{5}{3} = \frac{20}{3}\,\mathrm{V} \)
    \( V_B = 10 - 2\times\frac{10}{3} = \frac{10}{3}\,\mathrm{V} \)

    \( V_A - V_B = \frac{20}{3} - \frac{10}{3} = \frac{10}{3}\,\mathrm{V} \)