Book edition 1st Edition

Author(s) Paul Peter Urone

Pages 1272 pages

ISBN 9781938168000

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Short Answer

Apply the loop rule to loop abcdefgha in Figure 21.25

By applying Kirchhoff's loop rule in the loop abcdefgha, we get,

l_{1} = 18.5 A l_{2} = 2 A l_{3} = 16.5 A

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Definition of Kirchhoff's law

Kirchhoff's first law defines currents at circuit junctions. It states that the sum of currents flowing into and out of a junction in an electrical circuit equals the sum of currents flowing out of the junction.

Step 2: Given information and formula to be used

$\begin{array}{l} E_{1} = 18 V, R_{1} = 6 Ω, r_{1} = 0.5 Ω \\ E_{2} = 45 V, R_{2} = 2.5 Ω, r_{2} = 0.5 Ω \\ R_{3} = 0.5 Ω \end{array}$

And

We get the following results using Kirchhoff's loop rule:

$l_{2} R_{2} - E_{1} + l_{2} r_{1} + (l_{1} - l_{3}) R_{1} = 0$

and

$- E_{2} + l_{3} (r_{2}) + (l_{3}) (R_{3}) + (l_{1} - l_{3}) R_{1} = 0$

Step 3: Calculation of the current in the loop of abcdegfha

Apply the formula

$l_{2} R_{2} - E_{1} + l_{2} r_{1} + (l_{1} - l_{3}) R_{1} = 0$

Substituting the values in the above expression, we get

$l_{2} R_{2} - E_{1} + l_{2} r_{1} + (l_{1} - l_{3}) R_{1} = 0 l_{2} (2.5) - 18 + 0.5 (l_{2}) + 6 l_{2} = 0 Here (l_{1} - l_{3} = l_{2}) 9 l_{2} = 18 l_{2} = 2 A$

Now,

$- E_{2} + l_{3} (r_{2}) + (l_{3}) (R_{3}) + (l_{1} - l_{3}) R_{1} = 0$

Substitute the values in the above expression:

$2 l_{3} + 6 l_{2} = 45 2 l_{3} = 45 - 12 2 l_{3} = 33 l_{3} = 16.5 A$

Consider role="math" localid="1655960790613" $l_{2} R_{2} - E_{1} + l_{2} r_{1} + (l_{1} - l_{3}) R = 0$

Now substitute the value of $l_{1}$ and $l_{3}$ in the above expression which results in,

$l_{2} R_{2} - E_{1} + l_{2} r_{1} + (l_{1} - l_{3}) R = 0 5 - 18 + 1 + l_{1} (6) - 99 = 0 - 111 + 6 l_{1} = 0 6 l_{1} = 111 l_{1} = 18.5 A$

Hence,after applying the loop rule in loop 'abcdefgha' the values of currents are:

$l_{1} = 18.5 A l_{2} = 2 A l_{3} = 16.5 A$

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College Physics (Urone)

Answers without the blur.

Short Answer

Apply the loop rule to loop abcdefgha in Figure 21.25

Step by Step Solution

Step 1: Definition of Kirchhoff's law

Step 2: Given information and formula to be used

Step 3: Calculation of the current in the loop of abcdegfha

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College Physics (Urone)

Answers without the blur.

Short Answer

Apply the loop rule to loop abcdefgha in Figure 21.25

Step by Step Solution

Step 1: Definition of Kirchhoff's law

Step 2: Given information and formula to be used

Step 3: Calculation of the current in the loop of abcdegfha

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