Question

PHYS222 V2 Fullerton College Spring 2019 7· The 100μF capacitor in the circuit an ini resistor is 25t below has an initial charge of 1 HC. The switch is closed a. What is the charge on the capacitor as a c. What is th d. What is th e. How much energy is stored in the capacitor at function of time? otage on the capacitor as a function of time? e current in the circuit as a function of time? e rate of power dissipation in the resistor as a function of time? f. Abo ut how long do you need to wait for the capacitor to be effectively discharg

Answer 1

Discharging of capacitor: - let at any time 't' the capacitor has charge q Therefore using KVL Q_0 = 1 mc r = 250 Ohm c = 100 mu f q/c + ir = 0, c = dq/dt rightarrow dq/dt = - q/rc integral_q_0^q dq/q = - integral_0^t dt/rc q = q_0 e^- t/rc charge as a function of time q = q_0 e^- t/rc voltage of capacitor v_c = q/cd Therefore v_c = q_0 /c e^- t/rc current as a function of time i = dq/ft i(t) = - q_0/rc e^- t/rc power dissipation p = i^2 r = p(t) = q^2_0/rc^2 e^- 2t/Rc Therefore energy, e = integral_0^t p(t) dt, t = 20 ml = 0.25 rightarrow e = integral_0^0.02 q_0^2 /rc^2