Question

In the circuit, the potential difference between A and B is
Pls explain your answer.
Option (4) is the right answer.

Answer 1

The potential difference between A and B is 2V.

Consider the branch having two 8uF capacitors in parallel with a 4uF capacitor.

Effective capacitance = ( 8 and 8 in series ) parallel with 4.

8uF and 8uF in series gives an effective capacitance of 4uF.

4uF and 4uF in parallel gives an effective capacitance of 8uF.

Now,

Q = CV => Q proportional to 1/V

In series the voltage gets divided between the two capacitance 2uF and 4uF.

Since Q is inversely proportional to V,

Voltage across 8uF = 20 x 2/2+8 = 4V.

Now each branch in the 4uF parallel to 8uF in series has 4V across them.

Therefore VAB = Voltage across the effective 8uF divided by 2.

Therefore VAB = 4V x 8uF/8uF + 8uF = 4x1/2 = 2V.