Basic Engineering Circuit Analysis
Basic Engineering Circuit Analysis
11th Edition
ISBN: 9781118539293
Author: J. David Irwin, R. Mark Nelms
Publisher: WILEY
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Chapter 10, Problem 1P

Given the network in Fig. P10.1,

(a) write the equations for υ a ( t ) and υ b ( t ) .

(b) write the equations for υ c ( t ) and υ d ( t ) .

Chapter 10, Problem 1P, Given the network in Fig. P10.1, (a) write the equations for a(t)andb(t). (b) write the equations

a

Expert Solution
Check Mark
To determine

The equations for va(t) and vb(t) for the given circuit.

Answer to Problem 1P

The equations are:

  va(t)=L1di1(t)dtMdi2dtvb(t)=L2di2dtMdi1dt

Explanation of Solution

Given:

The given circuit is shown below.

Basic Engineering Circuit Analysis, Chapter 10, Problem 1P , additional homework tip  1

Calculation:

Referring to the given circuit, applying the Kirchhoff’s voltage law to the left side of the loop:

  va(t)+L1di1(t)dtMdi2(t)dt=0va(t)=L1di1(t)dtMdi2dt..........(1)

From the circuit:

  va(t)=vc(t)..........(2)

Solving equation 1 and 2:

  va(t)=vc(t)=L1di1(t)dtMdi2dt

Now applying the KVL to the right side of the loop:

  vb(t)L2di2dtMdi1dt=0vb(t)=L2di2dtMdi1dt............(3)

Therefore, the equation will be:

  va(t)=L1di1(t)dtMdi2dtvb(t)=L2di2dtMdi1dt

b

Expert Solution
Check Mark
To determine

The equations for vc(t) and vd(t) for the given circuit.

Answer to Problem 1P

The equations are:

  vc(t)=L1di1(t)dt+Mdi2dtvd(t)=L2di2dt+Mdi1dt

Explanation of Solution

Given:

The given circuit is shown below.

Basic Engineering Circuit Analysis, Chapter 10, Problem 1P , additional homework tip  2

Calculations:

From part (a), the equations of the va(t) and vb(t) are:

  {va(t)=L1di1(t)dtMdi2dtvb(t)=L2di2dtMdi1dt}..........(1)

From the circuit:

  {va(t)=vc(t) vb(t)=vd(t)}...............(2)

Hence, solving the equation:

  va(t)=vc(t)=L1di1(t)dtMdi2dtvb(t)=vd(t)=L2di2dtMdi1dt

Therefore, the equations are:

  vc(t)=L1di1(t)dt+Mdi2dtvd(t)=L2di2dt+Mdi1dt

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