An uncharged capacitor and a resistor are connected in series to a battery, as i

Question

An uncharged capacitor and a resistor are connected in series to a battery, as in Figure below. If 12.0 V, C 5.00 mu F, and R 8.00 Times 10^5 Ohm, find the time constant of the circuit, the maximum charge on the capacitor, the charge on the capacitor after 6.00 s, the potential difference across the resistor after 6.00 s, and the current in the resistor at that time. A 12.00-V battery is connected through a switch to two identical resistors and an inductor, as shown in the figure. Each of the resistors has a resistance of 100. Ohm, an ms an inductance of 4.00 H. The switch is initially open.

Explanation / Answer

a)

time constant T = Rc = 8*10^5*5*10^-6 = 4s

(b)

maximun charge Q = CV = 5*10^-6*12 = 60*10^-6 C

(c)

charge increases as q = Q*(1-e^-(t/T))

q = 60*10^-6*(1-e^-(6/4)) = 46.*10^-6 C

(d)

dv = iR = (V/R)*Re^-(t/T)

dV = V*e^-(t/T)

dV = 12*e^-(6/4)

dV = 2.7 v

(e)

i = dV/R = 3.375*10^-6 A

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