Basic Engineering Circuit Analysis
Basic Engineering Circuit Analysis
11th Edition
ISBN: 9781118992661
Author: Irwin, J. David, NELMS, R. M., 1939-
Publisher: Wiley,
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Chapter 7, Problem 1P

Use the differential equation approach to find i(t) for t > 0 in the network in Fig. P7.l.

Chapter 7, Problem 1P, Use the differential equation approach to find i(t) for t0 in the network in Fig. P7.l.

Expert Solution & Answer
Check Mark
To determine

The current i(t) for t>0 in the given circuit using the differential equation.

Answer to Problem 1P

iL(t)=2e3tA

Explanation of Solution

Given information:

Given circuit is shown below

Basic Engineering Circuit Analysis, Chapter 7, Problem 1P , additional homework tip  1

Fig: Given circuit diagram

Calculation:

Although for -t=0 inductor acts as short circuit, now draw the circuit for t=0 .

Basic Engineering Circuit Analysis, Chapter 7, Problem 1P , additional homework tip  2

Fig: Circuit diagram for t=0

iL(0)=126=2A

Now, draw the circuit when switch is opened at t =0.

Basic Engineering Circuit Analysis, Chapter 7, Problem 1P , additional homework tip  3

Fig: circuit diagram for t>0

Apply KVL for loop 1

2diL(t)dt+6iL(t)=0diL(t)dt=3iL(t)

Standard from of solution of above equation is

iL(t)=K2etτ

Plugging iL(t) into above equation.

K2etττ=3K2etττ=13

Therefore,

iL(t)=K2et13iL(t)=K2e3t(1)att=0 ,iL=2AiL(0)=K2e3×0K2=2

Now, from equation (1),

iL(t)=2e3tA

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