Question
Five capacitors of capacitances C_1 = C_2 = C_3 = C_4 = 10\ F and C_5 = 2.5\ F are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are :
Five capacitors of capacitances C_1 = C_2 = C_3 = C_4 = 10\ F and C_5 = 2.5\ F are connected as shown, along with a battery of 50 V. The equivalent capacitance and the charges on each capacitor respectively are :
B. 5\ F, 125\ C on all capacitors
From the given circuit diagram, the capacitors C_1, C_2, C_3, and C_4 are connected in series. This series combination is connected in parallel with the capacitor C_5. The entire combination is connected across the 50 V battery. Let C_s be the equivalent capacitance of the series branch containing C_1, C_2, C_3, and C_4. 1 C_s = 1 C_1 + 1 C_2 + 1 C_3 + 1 C_4 1 C_s = 1 10 + 1 10 + 1 10 + 1 10 = 4 10 \ F ^ -1 C_s = 2.5\ F The total equivalent capacitance C_ eq of the circuit is the sum of the parallel capacitances C_s and C_5: C_ eq = C_s + C_5 = 2.5\ F + 2.5\ F = 5\ F The voltage across the series branch is equal to the battery voltage, V = 50 V . The charge on the series combination is: Q_s = C_s V = 2.5\ F 50 V = 125\ C Since C_1, C_2, C_3, and C_4 are in series, they each carry the same charge Q_s. Therefore, charge on C_1, C_2, C_3, C_4 = 125\ C . The voltage across capacitor C_5 is also 50 V . The charge on C_5 is: Q_5 = C_5 V = 2.5\ F 50 V = 125\ C Thus, the equivalent capacitance is 5\ F and the charge on all capacitors is 125\ C . Answer: 5\ F, 125\ C on all capacitors
Related: Physics — Capacitance · All PYQ Banks