An uncharged capacitor and a resistor are connected in serie

An uncharged capacitor and a resistor are connected in series to a source of emf. If = 7.00 V, C-21.0 F, and R-100 , find the following (a) the time constant of the circuit ms (b) the maximum charge on the capacitor (c) the charge on the capacitor at a time equal to one time constant after the battery is connected

Solution

given

uncharged capacitor, C = 21 uF

E = 7 V

R = 100 ohms

a. time constant = t\' = RC

t\' = 100*21*10^-6 = 2.1*10^-3 s = 2.1 ms

b. maximum charge on capacitor = Q

Q = C/V = 21*10^-6/7 = 3 uC

c. at t = t\'

q = Q(1 - e^(-t/t\'))

q = Q(1 - 1/e)

q = 1.8963616 uC