Question

2. The two switches in the following circuit operate synchronously. When switch-1 is open switch-2 is in position a. When switch-1 is closed, switch-2 moves to position b. Switch been open for a long time and then closes at t-0. Find iz(t) for 120.(40) -1 has 5 0 o 51 1H (t) 8 V 1 H 5 H 24? a.

Answer 1

When switch s1 was open for a long line, hence switch s2 closed . t < 0 Applying KVL in loop 2, 5 - i^1_ 2 (5) - 5 di^1_ 2/dt = 0 Rightarrow Applying Laplace transform, 5 - I^1_ 2 (s) (5) - (5s) I^1_ 2 (s) = 0 Rightarrow 5 = (5 + 5 s) I^1_ 2 (s) Rightarrow I^1_ 2 (s) = 5/(5 + 5 s) = 1/(s + 1) Rightarrow i^1_ 2 (t) = e^- t i.e from - 10 to 0 i^1_ 2 (infinity) = 04 Again, v_ 1 (t) = di^1_ 2/dt At t = 0 when switch s1 was closed, applying KVL in loop 1, 8 - i_ 1 (8) - di_ 1/dt + di_ 2/dt = 0 Rightarrow di_ 1/dt - partial differential i_ 2/partial differential t + 8 i_ 1 = 8 \ r \ n Again, - 5 di_ 2/dt + di_ 1/dt - 24 i_ 2 = 0 In Laplace domain s I_ 1 (s) = 5 s I_ 2 (s) + 24