R = 7.1 x 10^5 [ohm] V = 12 [V] C = 4.1 x 10^-6 [micro Farads A capacitor In ser

Question

R = 7.1 x 10^5 [ohm]

V = 12 [V]

C = 4.1 x 10^-6 [micro Farads

A capacitor In series with a resistor, switch, and battery, When the switch is thrown to position a, the capacitor begins to charge up. When the switch is thrown to position b, the capacitor discharges. Evaluate the time constant of the circuit: Evaluate the maximum charge on the capacitor: Evaluate the maximum current in the circuit: Find the charge and current as functions of time (in seconds): (Use the following as necessary: t.) (Use the following as necessary: t.)

Explanation / Answer

Apply Kvl to the circuit when the switch position in a

E = R*I + (1/C) integral of I * dt

Apply Laplace transform

E(s)/s = (RCS+1)*I(s)/(CS)

I(s) = (E/R)* (1/(RCS+1)

APPLY INVERSE LAPLACE TRANSFORM

I(t) = (E/R)*e^-(t/RC)

I(t) = 12/(7.01*10^5) * e^-(t/2.911) = 16.9 * e^-(t/2.911)micro amps

q(t) = integral 0f (I(t)) = - (16.9/2.911) e^-(t/2.911) = 5.805 e^-(t/2.911) micro coulombs

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