Question

Four capacitors are connected in a circuit as illustrated. Find the charge on, the voltage difference across, and the energy stored for each of the capacitors.

tor? Four capacitors are connected in a circuit as 57. .. t as illas trated in ▼ Fig. 16.29. Find the charge on, thevas inu the ference across, and the energy stored for each of capacitors C1 0.40 μF 0.40 μF C3 CA 12 V 0.20 μF 0.60 μF

Answer 1

Capacitors C1 and C2 are in parallel. Hence their net capacitance C12 = (0.40 + 0.40) $\mu$ F = 0.80 $\mu$ F

Similarly, Net capacitance of C3 and C4 in parallel, C34 = (0.20 + 0.60) $\mu$ F = 0.80 $\mu$ F

Thus we have two equal capacitances C12 and C34 connected in series across 12 V supply. Hence potential difference acros each capacitance C12 and C34 is 6 V. As C1 and C2 are in parallei and C3 and C4 in parallel, therefore

P.D. across C1 = P.D. across C2 = P.D.across C3 = P.D. across C4 = 6 V

Charge on C1 = Charge on C2 = (0.4 $\mu$ F) x 6 V = 2.4 $\mu$ C

Charge on C3 = (0.20 $\mu$ F) x 6 V = 1.2 $\mu$ C

Charge on C4 = (0.60 $\mu$ F) x 6 V = 3.6 $\mu$ C

Energy stored in C1 = Energy stored in C2 = (CV²) / 2 = (0.40 $\mu$ F) x 36 V ² / 2 = 7.2 $\mu$ J

Energy stored in C3 = (CV²) / 2 = (0.20 $\mu$ F) x 36 V ² / 2 = 3.6 $\mu$ J

Energy stored in C4= (CV²) / 2 = (0.60 $\mu$ F) x 36 V ² / 2 = 10.8 $\mu$ J