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 3.0 microfarad capacitor in parallel with the 10 ohm resistor or opened to disconnect the capacitor from the circuit. (Use 2 sig. figs, throughout.) Case 1: 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

Case 1 :

In this case the capacitor is cut off from the circuit .

So, net resistance of the circuit : Rnet = (2+10) || 4+ 6

= 12 * 4/(12+4) + 6

= 9 ohm

So, current in the battery = 72/9 = 8 A <----answer(a)

b)

current in 10 ohm resistor = (72 - 8*6)/12 = 2 A <-----answer (b)

c)

Potential difference across 10 ohm = 2*10 = 20 V

CASE II :

d)

Charge on the capacitor = 20*3 = 60 uC

e)

energy stored in the capacitor = 0.5*(3u)*20^2

= 600 uJ

= 6*10^-4 J

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