A circuit diagram is shown in the above figure (left). The capacitors have the f

Question

A circuit diagram is shown in the above figure (left). The capacitors have the following capacitance values C_1 = 7F and C_2 = 10F. The resistors have the following resistance values R_1 = 7 ohm and R_2 = 10 ohm. (a) Determine the equivalent capacitance in the circuit (Reduce the problem to a single capacitor.) (b) Determine the equivalent resistance in the circuit. (Reduce the problem to a single resistor.) (c) Determine the time constant of the RC circuit. (d) After some time the capacitor is charged and current is no longer flowing. The battery has a voltage rating of 24V. Determine the charge on the capacitor.

Explanation / Answer

(a)

equivalent capacitance Ceq = C1 + C2 = 7 + 10 = 17 F

(b)

equivalent resistance Req = (R1*R2)/(R1+R2)

Req = (7*10)/(7+10) = 4.12 ohm

(c)

time constant T = Req*Ceq = 4.12*17 = 70.04 s

(d)

charge on capacitor1 = Q1 = C1*V = 7*24 = 168 C

charge on capacitor2 = Q2 = C2*V = 10*24 = 240 C

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