A 6 F capacitor is connected in series with a parallel combination of two capacitors of capacitances 2 F and 1 F . This entire arrangement is connected across an 18 V battery. The charge on the 2 F capacitor is

Step-by-step solution

First, find the equivalent capacitance of the parallel combination of the 2 F and 1 F capacitors: C_p = 2 F + 1 F = 3 F This combination is in series with the 6 F capacitor. The total equivalent capacitance of the circuit is: C_ eq = 6 3 6 + 3 = 18 9 = 2 F The total charge supplied by the battery is: Q_ total = C_ eq V = 2 F 18 V = 36 C This total charge flows through the 6 F capacitor and then splits into the parallel branches. The voltage across the parallel combination is: V_p = Q_ total C_p = 36 C 3 F = 12 V Th