Problem

Find io in the circuit shown in Fig.10.85 using superposition.Figure10.85For Prob.10.40.

Find io in the circuit shown in Fig.10.85 using superposition.

Figure10.85

For Prob.10.40.

Step-by-Step Solution

Solution 1

Refer to Figure 10.85 in the textbook.

The circuit is operating at two different frequencies, i.e. (for DC source) and . Use the super position principle to break the given problem into single frequency problem.

Assume that the total current due to acting of both sources is,

Here,

is the response due to DC source and

is the response due to AC source.

To find , set ac source value to zero. In a steady state inductor acts like a short circuit, so replace an inductor with circuit. Draw the modified circuit diagram.

$C:\Users\phaneendra\Desktop\a.jpg$

Since resistor is comes in parallel with short circuit, the total current will flow through short circuit only. Calculate the value of current .

Therefore, the current response due to DC source is .

To find , set dc source value to zero and transform the circuit into frequency domain.

The value of angular frequency is,

The phasor representation of ac source is,

Calculate the inductive reactance of 1 H inductor.

Draw the circuit diagram in frequency domain.

$C:\Users\phaneendra\Desktop\d.jpg$

In Figure 2, the parallel combination of and is in series with resistor. Determine the total impedance of the circuit.

Calculate the total current in the circuit.

Calculate the value of current using current division principle.

Convert the current into time domain.

Determine the total current by adding both the responses.

Therefore, the value of current is .

Add your Solution

Textbook Solutions and Answers Search

Solutions For Problems in Chapter 10

95P
96P

ADVERTISEMENT

Free Homework Help App

Download From Google Play

Scan Your Homework
to Get Instant Free Answers

Need Online Homework Help?

Get Answers For Free
Most questions answered within 3 hours.

ADVERTISEMENT

Recent Solutions