A capacitor of capacitance 4 F is connected in series with another capacitor of 12 F . This series combination is connected in parallel with a third capacitor of 5 F . If the entire arrangement is connected across a 20 V battery, what is the charge on the 4 F capacitor and the total electrostatic energy stored in the circuit, respectively?

Step-by-step solution

Equivalent capacitance of the series combination of 4 F and 12 F is: C_s = 4 12 4 + 12 = 48 16 = 3 F The charge on the 4 F capacitor is the same as the charge on this series branch, since capacitors in series carry the same charge. The voltage across the series combination is the battery voltage, 20 V . Q = C_s V = 3 F 20 V = 60 C The total equivalent capacitance of the circuit is the parallel combination of C_s and the 5 F capacitor: C_ eq = 3 F + 5 F = 8 F The total electrostatic energy stored in the circuit is: