Solution Found!
The circuit shown in Figure P 14.6-3 is at steady state before time t 0. The input to
Chapter 14, Problem P14.6-3(choose chapter or problem)
The circuit shown in Figure P 14.6-3 is at steady state before time t = 0. The input to the circuit is
\(v_s(t)=2.4 u(t) \mathrm{V}\)
Consequently, the initial conditions are \(i_1(0)=0\) and \(i_2(0)=0\). Determine the inductor current \(i_2(t)\) after time t = 0.
Questions & Answers
QUESTION:
The circuit shown in Figure P 14.6-3 is at steady state before time t = 0. The input to the circuit is
\(v_s(t)=2.4 u(t) \mathrm{V}\)
Consequently, the initial conditions are \(i_1(0)=0\) and \(i_2(0)=0\). Determine the inductor current \(i_2(t)\) after time t = 0.
ANSWER:
Step 1 of 4
Initially there are no currents in the circuit,
and
or
is applied to the circuit, then to determine the inductor current, recall that current and voltage for an inductor are related as
Step 2 of 4
By applying KVL in the circuit, we get
..............(1)
………..(2)
By taking Laplace and solving the equations, we get following relations.