An uncharged capacitor and a resistor are connected in serie

An uncharged capacitor and a resistor are connected in series to a battery. If 12.0 V, C= 6.00uF, and R=4.00 x10^5 ohms, find:

a) the time constant of the circuit.

b) the maximum charge on the capacitor.

c) the charge on the capacitor after 4.00 s.

d) The potential difference across the resistor after 6.00 s

e) The current in the resistor at that time.

Thank You ! :)

a) Time constant = R C

= (4 x 10^5 ) ( 6 x 10^-6) = 2.4 s

b) Maximum charge on capacitor will be when capacitor is fully charged.

when fully charged then PD cross capacitor, V0 = 12 V

Qmax = C Vmax = 6 x 10^-6 x 12 = 72 x 10^-6 C = 72 uC

c) For charging,

Q = Qmax [ 1 - e^(-t/T) ]

Q = 72 uC [ 1 - e^(-4/2.4)]

Q = 58.4 uC

d) Vc = Vmax [ 1 - e^( - t / 2.4) ]

Vc = 12 [ 1 - e^(-6/2.4)]

Vc = 11.01 Volt ....PD across capacitor.

PD across resistor = 12-11.01 = 0.985 volt

e) I = Vr / R = 0.985 / (4 x 10^5) = 2.46 x 10^-6 A