A capacitor of capacitance C = 55 mu F initially uncharged. It is connected in s

Question

A capacitor of capacitance C = 55 mu F initially uncharged. It is connected in series with a switch of negligible resistance, a resistor of resistance R = 75 k Ohm, and a batter)' which provides a potential difference of = 165 V. (a) Immediately after the switch is closed, what is the voltage drop V_C, in volts, across the capacitor? Part (b) Immediately after the switch is closed, what is the voltage drop in volts, across the resistor? Part (c) Immediately after the switch is closed, what is the current I, in amperes, through the resistor? (d) Find an expression for the time t_1/2 after the switch is closed when the current in the resistor equals half its maximum value. (e) What is the charge Q, in microcoulombs, on the capacitor when the current in the resistor equals one half its maximum value.

Explanation / Answer

a)

Vc = VB(1-e-t/RC)

At t=0s,

Vc = VB(1-e0)

Vc = VB(1-1)

Vc = VB

b)

VB = Vc + VR

VR = Vc

c)

IR = VB/R = 165/7500 = 0.022 A

d)

I1/2 = Ic = IR(1-e-t’/RC)

0.5 = (1-e-t’/(7500*0.000055))

t' = 0.286s

e)

Vc = 165(1-e-0.286/(7500*0.000055))

Vc = 82.5 V

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