Question

The triangular current pulse is applied the four time intervals, t0, 0 st< 5 ms, 5 ms ts 10 ms, and to a 20 mH inductor. (a) Write the expressions that describe it) in IS t> 10 ms. (b) Derive the expressions for inductor voltage, power and energy. Use passive sign convention i(mA) 250 10ms t(ms 5ms

Answer 1

Given Data (a) L = 20 mH From the given triangular pulse For t < 0 i(t) = 0 For 0 lessthanorequalto t lessthanorequalto 5 ms: i(t) = (250/5)t = 50 t For 5 ms lessthanorequalto t lessthanorequalto 10 ms i(t) = -(250/5)t + c i(t) = -50t + c At t = 10 ms: i(t) = 0 D = -50t + C C = 50 t = 50 times 10 = 500 ms. i(t) = -50t + 500 m (b) Inductor voltage = v(t) = L middot di(t)/dt L = 20 mH For t < 0: v(t) = 20 times 0 = 0 v For 0 lessthanorequalto t lessthanorequalto 5 ms: v(t) = 20 times 10^-3 times d/dt (50 t) = 20 times 10^-3 times 50 = 1v. \r\n For 5 ms lessthanorequalto t lessthanorequalto ms = i(t) = -50t + 500 m v(t) = 20 times 10^-3 times d/dt (-50t + 500) = 20 times 10^-3 times -50 = -1V. Calculation of Power We know Power = v(t) middot i(t) For t < 0 p(t) = i(t) middot v(t) = 0 \r\n