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

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 = 705.0 the capacitor has capacitance of C = 97.0 F and the battery maintains the emf of = 19.0 V. The switch is closed at time t = 0.0 s and the capacitor begins to charge. A. What is the time constant for this circuit? B. What is the charge on the capacitor after the switch has been closed for t = 4.45×10-2 s? C. What is the current through the circuit after the switch has been closed for t = 4.45×10-2 s? D. What is the voltage across the capacitor after the switch has been closed for t = 4.45×10-2 s?

Explanation / Answer

A) time constant = RC = 705 x 97 x 10^-6 = 0.0684 s

B) V = V0 [ 1 - e^(-t /RC)]

V = 19 [ 1 - e^(-0.0445 / 0.0684) ]

V = 9.09 Volt

Q = CV = 97 uF x 9.09 = 881.57 uC

C) I = (e - Vc) / R = (19 - 9.09) / 705 =0.014 A = 14 mA

d) V = 9.09 V

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