Question

A series RC circuit has a 12 volt battery connected in series to a resistor with resistance 1 ?? and a capacitor wi capacitor. The switch is thrown at t-0 seconds. a) Write the differential equation for the circuit. b) Solve the equation for the charge q() and the current io). 8. th capacitance 1 pF. There is an initial charge of 10 nC on the

Answer 1

The initial charge q = Q initial time t = 0 using the KVL epsilon = q/c - IR = 0 while discharging no voltage in the circuit the circuit eqn becomes - q/c IR = 0 therefore I = dq/dt - R dq/dt = q/c implies dq/dt = -q/RC b. dq/dt = -q/RC - dq/q = 1/RC - ln Q + ln (q) = -t/RC q(t) = Qe^- t/RC & I(t) dq/dt = -Q/RC e^- t/RC implies I(t) = -Q/RC e^- t/RC