Three capacitors with capacitances of 20 F , 30 F , and 40 F are connected in series across a 12 V battery. Determine the charge acquired by each capacitor and the work done by the battery during the charging process.

Step-by-step solution

The equivalent capacitance C_ eq for capacitors connected in series is given by: 1 C_ eq = 1 C₁ + 1 C₂ + 1 C₃ 1 C_ eq = 1 20 + 1 30 + 1 40 = 6 + 4 + 3 120 = 13 120 F ⁻¹ C_ eq = 120 13 F In a series circuit, the charge Q on each capacitor is the same and is equal to the total charge supplied by the battery: Q = C_ eq V = ( 120 13 F ) 12 V = 1440 13 C The work done by the battery during the charging process is given by W = QV : W = ( 1440 13 10⁻⁶ C ) 12 V = 17280 13 10⁻⁶ J W 1329.23 10⁻⁶ J = 1.33 10⁻³ J