Question

Specify the numerical value of I, Express your answer to three significant figures and include the appropriate units. ReviewI Constants The current and voltage at the terminals of the capacitor in the circuit in (Figure 1) are i(t) 2.5e2500f mA, vt)- (40 22e 25t) V, t20 I6.36 mA where t is in seconds. SubmitP XIncorrect; Try Again Part B Specify the numerical value of Vo Express your answer to three significant figures and include the appropriate units. 18.0 V Figure 1 of 1 Correct Part C Specify the numerical value of R Express your answer to three significant figures and include the appropriate units.

Answer 1

Given i(t) = 2.5 e^-2500 t times 10^-3 A v(t) = (40 - 22 e^-2500 t) v for RC circuit v = I_s R + (V_0 - I_s R) e^-t/RC compare equation I_s R = 40 V_0 - I_s R = -22 V_0 = -22 + 40 = 18 v i = (I_s - V_0/R) e^-t/tau I_s - V_0/R = 2.5 times 10^-3 = > I_s - 18/R = 2.5 times 10^-3 Therefore [I_s = 40/R] 40/R - 18/R = 2.5 times 10^-3 = > 22 = 2.5 times 10^-3 R R = 22/2.5 times 10^-3 = > R = 8.8 k Ohm I_s = 40/R = 40/8.8 k = 4.54 mA I_s = 4.54 mA 1/RC = + 2500 = > C = 1/2500 times 8.8 times 10^+ 3 = 45.45 times 10^-9 C = 45.45 nf tau = RC = m 1/2500 = 400 mu s = 400 mu s At t = infinity v(infinity) = 40 - 22 e^- infinity = 40 v w(infinity) = 1/2 cv^2 = 1/2 times 45.45