1. Four capacitors are connected to a battery as shown in the figure below. The

Question

1. Four capacitors are connected to a battery as shown in the figure below. The four capacitors have capacitance values of Ci3.00 nF, C22.00 nF, C3 4.00 nF, and C46.00 nF. The potential difference of the battery is 15.0 V. There is a switch in the circuit that is initially open. (a) Before the switch is closed, how much energy is supplied to the circuit by the battery? Os 3 (b) After the switch is closed, how much energy is supplied to the Vl circuit by the battery once the capacitors are fully charged? C.

Explanation / Answer

A.

Before the Switch is closed

C1 and C2 are in Series

Ceq = C1*C2/(C1 + C2)

Ceq = 3*2/(3 + 2) = 6/5 nF

Energy Supplied = 0.5*Ceq*V^2

Enet = 0.5*(6/5)*10^-9*15^2 = 1.35*10^-7 J

B.

After the Switch is closed

C3 and C4 are in Series

C34 = C3*C4/(C3 + C4)

C34 = 4*6/(4 + 6) = 2.4 nF

C34 and C2 are in parallel

C234 = 2 + 2.4 = 4.4 nF

C1 ad C234 are in Series,

Ceq = 3*4.4/(3 + 4.4) = 1.784 nF

Energy Supplied = 0.5*Ceq*V^2

Enet = 0.5*1.784*10^-9*15^2 = 2.01*10^-7 J

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