The circuit shown above includes a switch S, which can be closed to connect the

Question

The circuit shown above includes a switch S, which can be closed to connect the 3-microfarad capacitor in parallel with the 10-ohm resistor or opened to disconnect the capacitor from the circuit.

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Case I. Switch S is open. The capacitor is not connected. Under these conditions determine:
a) The current in the battery
b) the current in the 10-ohm resistor
c) the potential difference across the 10-ohm resistor

Case II. Switch S is closed. The capacitor is connected. After some time, the currents reach constant values. Under these conditions determine:
d) The charge on the capacitor
e) The energy stored in the capacitor

Explanation / Answer

Resistance of 2 and 10 are in series - R2,10 R2,10 = 2+10 = 12 Resistance of the combination 2,4 and 10 - R4,2,10 1/ R4,2,10 = 1/ 4 + 1/12 = 3 R total = 6+3 = 9 I battery = V/R = 72V/ 9 I battery = 8 A
(b) The current in the 10 resistor V2,10 = 72 V - (6)(8A) = 24 V I 10 = I 2,10 = 24 V/12 I 10 = 2 A
(c) The potential difference across the 10 resistor V10 = I10 R10 = (2A)(10) = 20 V V10 = 20 V
Case II. Switch S is closed. The capacitor is connected. After some time, the currents reach constant values.
(d) The charge on the capacitor C = Q / V Q = CV = (3*10-6 F)(20 V) Q = 60 F
(e) The energy stored in the capacitor Energy = U = 1/2 CV2 U = 1/2 (3*10-6 F)(20V)2 = 6*10-4 J U = 6*10-4 J

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