a 3.0E6 resistor is connected in series with an initailly uncharged 0.28E-6 F ca

Question

a 3.0E6 resistor is connected in series with an initailly uncharged 0.28E-6 F capacitor. This arrangement is then connected across four 1.5 V batteries (also in series).

What is the maximum current in the circuit and when does it occur?

What percentage of the maximum current is in the circuit after 4.0s?

What is the maximum charge on the capacitor and when does it occur?

What percentage of the maximum charge is on the capacitor after 4.0s?

How much energy is stored in the capacitor after one time constat has elapsed?

Explanation / Answer

Maximum current is at t = 0 s

Maximum current = i_o = V/R = 4*1.5 / 3.0E6 = 2*10^-6 A

TIme constant = R*C = 0.84 s

i = i_o *e^ (-t/R*C)

After 4s , i = 8.549*10^-3 i_o

Current = 0.8549 percent of i_o

Maximum charge on capacitor, Q_o = C*V = 0.28E-6*(4*1.5) = 1.68 * 10^-6 C, this charge occurs at infinite time.

Q = Q_o ( 1- e^ (-t/R*C)) = 0.99145 * Q_o

After 4s, capacitor is charged to 99.14 % of Q_o.

Energy store in capacitor after 1 time constant

Q = Q_o (1- e^(-1)) = 0.632*Q_o

Energy = Q^2 / 2*C = (0.632^2) * (Q_o)^2/ 2*C = 2.01 * 10^-6 J

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