b A 2103uF capacitor with an initial charge of 5lpC is disch

(b) A 2×10-3-uF capacitor with an initial charge of 5.lpC is discharged through a 1300- resistor (a) Calculate the current through the resistor 9 us after the resistor is connected across the terminals of the capacitor. (b) What charge remains on the capaci- tor after 8? (c) what is the maximum current through the resistor?

Solution

a) the formula for RC circuit and charge in capacitor is

q = q_o (1-e^{t/RC )}

for 50% charge

Put q= q_o /2 , and we will get

=>1/2 = 1 - e^-t/RC

^=>e^-t/RC = 1/2

^=> -t/ RC = ln 1/2

=> t = RC ln 2

b) For complete charge

Put q = qo , and we will get

=> 1 = 1 - e^-t/RC

So in reality the capacitor never becomes 100% charges as t is edging to infinity here in this equation.