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An RC circuit, hooked up to a battery as shown in the figure, starts with an unc

ID: 1321307 • Letter: A

Question

An RC circuit, hooked up to a battery as shown in the figure, starts with an uncharged capacitor. The resistance in the circuit is R = 633.0 ? the capacitor has capacitance of C = 47.0 ?F and the battery maintains the emf of ? = 31.0 V. The switch is closed at time t = 0.0 s and the capacitor begins to charge.

What is the time constant for this circuit?

What is the charge on the capacitor after the switch has been closed for t = 4.0810-2 s?

What is the current through the circuit after the switch has been closed for t = 4.0810-2 s?

What is the voltage across the capacitor after the switch has been closed for t = 4.0810-2 s?

An RC circuit, hooked up to a battery as shown in the figure, starts with an uncharged capacitor. The resistance in the circuit is R = 633.0 ? the capacitor has capacitance of C = 47.0 ?F and the battery maintains the emf of ? = 31.0 V. The switch is closed at time t = 0.0 s and the capacitor begins to charge. What is the time constant for this circuit? What is the charge on the capacitor after the switch has been closed for t = 4.08½10-2 s? What is the current through the circuit after the switch has been closed for t = 4.08½10-2 s? What is the voltage across the capacitor after the switch has been closed for t = 4.08½10-2 s?

Explanation / Answer

Maximum Current

Imax=E/R =31/633 =0.04897 A

Maximum Charge

Qmax=CE =(47*10-6)*31=1.457*10-3 C

a)

Time Constant

T=RC=633*(47*10-6)

T=0.02975 s or 29.75 ms

b)

Charge on the capacitor as a function of time is given by

Q=Qmax[1-e-t/T] =(1.475*10-3)[1-e-0.0408/0.02975]

Q=1.1*10-3 C or 1.1 mC

c)

Current in a RC circuit as a function of time is given by

I=Imaxe-t/T =(0.04897)*e-0.0408/0.02975

I=0.01243 A or 12.43 mA

d)

Voltage across capacitor is

V=Vmax[1-e-t/T]=31[1-e-0.0408/0.02975]

V=23.13 Volts

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