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

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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.

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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.

     

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