Question

Homework S: ECE 235/ENGR335 Row Column. 1. For an inductor with inductance L-1H the voltage is given by the following function ov, tso ov, 10s <t If for tco, the current through the inductor is 1A give the function for the current through the inductor. 2. For a capacitor with capacitance C-1F the current is given by the following function. 0A, 1A, If for te0, the voltage across the capacitor is OV give the function for the voltage across the tso 1s<t capacitor 3. For a capacitor with capacitance C-1F the voltage is given by the following function. oV, tso u(t) =160V _ 4 . t-, 10s < t 15s Give the function for the current of the capacitor.

Answer 1

Given: L = 1H v(t) = {0v t lessthanorequalto 0 4v 0 < t lessthanorequalto 10s 0v 10s < t} for inductor i(t) = 1/L integral^t_-infinity i(t)dt for t < 0 i(t) = 1A (given) integral^s_2_s_1 x dt + integra^s_3 s_2 x dt = integral^s_3_s_1 x dt 0 < t < 10 i(t) = 1/1 [integral^0_-infinity v(t)dt + integral^t_0 v(t)dt] i(0^-) = i(t < 0) = 1 + integral^t_0 4 dt because v(t) for 0 to 10 to 4 i units ampere i(t) = 1 + 4t implies 1A + 4t a/s t > 10 i(t) = integral^0_-infinity v(t)dt + integral^10_0 v(t) dt + integral^t_10 v(t) dt = i(0^-) + integral^10_0 4 dt + integral^t_10 0 dt = 1 + 4 times 10 + 0 = 41A i(t) = {1A t < 0 1A + 4t 0 < t < 10s 41A 10s < t} 1 + 4t rightarrow 1A + 4t A/s finally units will be Amperes