An uncharged capacitor and a resistor are connected in serie

An uncharged capacitor and a resistor are connected in series to a battery, as in Figure below. If 12.0 V. C 5.00 muF, and R 8.00 times 10^5 ohm. find (a) the time constant of the circuit, (b) the maximum charge on the capacitor, (c) the charge on the capacitor after 6.00 s. (d) the potential difference across the resistor after 6.00 s. and (e) the current in the resistor at that time.

Solution

a)

time constant of the circuit:

T = R*C = 8*10^5*5*10^-6 = 4 s

b)

Maximum charge on the capacitor:

Qo = C*V = 5*10^-6*12 = 6*10^-5 C

c)

Charge on the capacitor is given by :

Q = Qo*(1 - e^(-t/T))

= 6*10^-5*( 1 - e^(-6/4))

= 4.66*10^-5 C

d)

Potential difference across resistors :

V = Vo - Q/C = 12 - 4.66*10^-5/(5*10^-6)

= 2.68 V

e)

Current in the resistor :

I = Io*e^(-t/T)

where Io = Vo/R = 12/(8*10^5) = 1.5*10^-5 A

So, I = 1.5*10^-5*e^(4/6)

= 2.92*10^-5 A