Question

01 The capacitor in the circuit to the left below is initially uncharged. It is connected to a voltage source that produces a voltage given to the right in the figure below. Plot the current through the capacitor as a function of time. Label your plot, write values and units it v(V) 10 HF 02 The switch in the circuit below is closed at time t 0 Sec. The initial voltage across the capacitor is zero. Find the current through the capacitor in the form of an equation. .70 1K 1ον 0.001 mF

Answer 1

i(t): - i(t) = c (dv/dt) rightarrow for a capacitor v(t): - for (0, 2) interval v(t) = (0, 2) (2, 1) rightwardsdoublearrow v(t) - y_1 = m(t - x_1) v(t) = 1/2 t 0 lessthanorequalto t < 2 for (2, 4) interval v(t) = 1 for (4, 5) interval rightarrow (4, 1) (5, 0) v(t) - 1 = -1/1 (t - 4) v(t) = -t + 5 0 lessthanorequalto t lessthanorequalto 5 v(t) = {t/2 0 lessthanorequalto t lessthanorequalto 2 1 2 lessthanorequalto t lessthanorequalto 4 5 - t 4 lessthanorequalto t lessthanorequalto 5 i(t) = c (dv/dt) i(t): 0 lessthanorequalto t lessthanorequalto 2 i(t) = 10 mu F (d/dt (t/2)) = 10 mu F times 1/2 v/mu s = 5 Amp \r\n i(t): 2 lessthanorequalto t lessthanorequalto 4 i(t) = c dv/dt = 10 mu F d/dt (1) i(t) = 0 Amp i(t): 4 lessthanorequalto t lessthanorequalto 5 i(t) = 10 mu F times d/dt (5 - t) = 10 mu F times (-1) v/mu s i(t) = -10 Amp The switch in the circuit below is closed at time t = 0 sec.