In an RC circuit EMF=120V, R= 1.40ohm m, and C=1.80pico F 11. (20 points) In an

Question

In an RC circuit EMF=120V, R= 1.40ohm m, and C=1.80pico F 11. (20 points) In an RC series circuit EMFs 120.0 V, R = 1.40 Ma, and C-1.80 (a) Calculate the time constant. (b) Find the maximum charge that will appear on the capacitor during charging. (c) How long does it take for the charge to build up to 20 uC? (d) What is the maximum current through the resistor? (e) What is the potential difference across the capacitor after it has been charging for 1.0 sec? (f) Sketch the charge and current as functions of time. (g) After being totally charged, the capacitor is carefully disconnected from the circuit above without discharging it. It is connected to a 520 kQ resistor and begins to discharge. What is the time constant for this circuit? (h) What will be the potential difference across the capacitor after 400 msec? (i) Sketch the charge and current as functions of time.

Explanation / Answer

a)

here

R = 1.40 * 10^6 ohm

C = 1.80 * 10^-6 F

V = 120 V

the time constant T

T = R * C

T = 1.4 * 10^6 * 1.8 * 10^-6

T = 2.52 sec

so the time constant is 2.52 sec

b)

then by using the formual

Q = C * V

Q = 1.8 * 10^-6 * 120

Q = 2.16 * 10^-4 C

so the maximum charge that will appear on the capacitor is 2.16 * 10^-4 C

c)

here by using the formula

Qc = Q (1 - e^-t /T)

Qc = 20 * 10^-6 C

Q = 2.16 * 10^-4 C

T = 2.52 sec

then put these values in the formula and get t

t = 0.245 sec

so the time taken t= 0.245sec

e)

here

Vc = V * ( 1 - e^-t /T)

Vc = 120 * ( 1 - e^- 1 / 2.52 )

Vc = 39.3 V

so the potential difference across the capacitor after 1 sec is 39.3 sec

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