capacitance C-85 HFis in It is connected in series with a switch of negligible r

Question

capacitance C-85 HFis in It is connected in series with a switch of negligible resistance, a resistor of resistance R-115 kS2, and a battery which provides a potential difference of VB 120 v ©theexpertta.com -? 20% Part (a) Immediately after the switch is closed, what is the voltage drop V , in volts across the capacitor? ??20% Part (b) Immediately after the switch is closed, what is the voltage drop VR, in volts, across the resistor? ?? 20% Part (c) Immediately after the switch is closed, what is the current I, in amperes, through the resistor? ??20% Part (d) Find an expression for the time 2 after the switch is closed when the current in the resistor equals half its maximum value. 20% Part (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 = 0

(Capacitor acts as a conducting wire just after switch is closed)

B) Since no voltage drop occurs the capacitor, so voltage drop across resistor is equal to VR = 120 V

c) I = VB/R = 120/(11.5 x 1000) = 0.010 A

D) I = VB/R * e(-t/RC)

at t1/2   I = VB/2R

so 1/2 = e(-t/RC)

t1/2 = RC*ln(2)

E) Q = CV

V = VB(1-e(-ln(2)RC/RC))

V = 120 (1 - 0.5) = 60 V

Charge, Q = CV = 60 x 8.5 x 10^-6 = 510 uC

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