Four capacitors are arranged in the circuit shown in the figure. The capacitors

Question

Four capacitors are arranged in the circuit shown in the figure. The capacitors have the values C1-27.5 F, C2 = 45.5 F, C3 = 50.5 F Ca = 40.5 F, and the power supply is at voltage V-25.5 V. What is the equivalent capacitance of the circuit? Number C. 14.42 What is the charge on capacitor C2? Number 3.68x 10 -4 What is the potential difference across capacitor C3? Incorrect. When capacitors are in parallel and a voltage is applied across the Number roup, the voltage across each capacitor in the group will be equal to 3.83 the voltage across the parallel equivalent capacitor. Also, a group of capacitors in series will all have the same charge that is in series with C1 and C2 What is the potential energy stored i However, keep in mind that it is the parallel combination of C3 and Ca Number 2.97x 10-4

Explanation / Answer

(a)

C3 and C4 are parallel,

C34 = 50.5 + 40.5 = 91 uF

This is in series with C1 and C3,

1 / Ceq = 1 / C1 + 1 / C2 + 1 / C34

1 / Ceq = 1 / 27.5 + 1 / 45.5 + 1 / 91

Ceq = 14.42 uF

(b)

Total charge in circuit, Q = Ceq*V

Q = 14.42 * 25.5 = 367.80 uC

charge on C2 = Q = 367.80 uC

Q2 = 3.68*10^(-4) C

(c)

Potential difference across C3,

V3 = Q / C34 = 367.80 / 91

V3 = 4.041 V

(d)

Potential energy stored in C4,

U4 = (1/2)*C4*V4^2

V4 = V3 = 4.04` V

U4 = (1/2)*40.5*(4.041)^2

U4 = 330.80 uJ

U4 = 3.31*10^(-4) J

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