Calculate the potential difference V_a - V_b between points a and b for the circuit labeled (b) as shown in the figure.

Step-by-step solution

The circuit labeled (b) is a single closed loop containing two capacitors and two batteries. The equivalent capacitance C_ eq of the 2 F and 4 F capacitors in series is C_ eq = 2 4 2 + 4 = 4 3 F . Traversing the loop in the clockwise direction, the 12 V battery acts to drive current clockwise, while the 24 V battery opposes it. The net electromotive force is E _ net = 24 - 12 = 12 V in the counter-clockwise direction. The steady-state charge Q on the equivalent capacitor is Q = C_ eq E _ net = ( 4 3 )(12) = 16 C .