Question

4)

Find the current i(t) in the circuit, when i(0)-1A and the voltage is as shown in the graph i(t) -att a2 for Os<t<1s for 1s<t<4s for 4 s<t<9s for 9 s <t i(t) ast + a6 8 vs(V) i(t) 1 2 3 5 6789t(s)

Given Variables:

L1 : 0.1 H

Determine the following:

a1 (A/s) :

a2 (A) :

a3 (A/s) :

a4 (A) :

a5 (A/s) :

a6 (A) :

a7 (A/s) :

a8 (A) :

Answer 1

From the given wave from of voltage it can be defined V_s (t) = -1 V, 0 < t < 1 -2 V, 1 < t < 4 1 V 4 < t < 9 -1 V, t > 9 we know the current voltage relation of inductor as V - 2 = L di/dt or i = 1/l integral^t_- infinite v dt i (t) = i (0) + 1/l integral^t_0 v dt given initial current i (0) = 1A Therefore from the price wise analysis of voltage wave length n i - 1 (t) = i (t) = i (0) + 1/L integral^t_0 v (t) dt 1 + 1/0.1 integral^t_0 (-1) dt = 1 + 10 (-t) = 1 - 10 t i_2 (t) = i (t) = 1 + 1/0.1 integral^t_1 (-2) dt