Question

find the potential difference across AB and AC​

Answer 1

Net EMF in the circuit (going anti-clockwise across the loop): E + E - E + E = 2E

Net resistance = 4r.

Current = 2E/4r = E/2r.

Going from B to A:

V(B) - ir + E = V(A)

V(B) - V(A) = ir - E = (E/2r)r - E = E/2 - E = -E/2.

$V_{AB} = -\frac{E}{2}$

Going from C to A:

V(C) - ir - E - ir + E = V(A)

V(C) - V(A) = 2ir = 2(E/2r)r = E

$V_{AC} = E$