Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

In Fig. 25-29, find the equivalent capacitance of the combination. Assume that $C_{1} = 10.0 μF$ , $C_{2} = 5.00 μF$ and $C_{3} = 4.00 μF$

The equivalent capacitance of the combination is 3.16 $μF$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

The capacitance $C_{1} = 10.0 μF$

The capacitance $C_{2} = 5.00 μF$

The capacitance $C_{3} = 4.00 μF$

Step 2: Determining the concept

Using the equation 25-19, find the equivalent capacitance of C₁ and C₂. Then using 25-20, find the equivalent capacitance of the given combination.

Formulae are as follows:

Capacitors in series combination,

$\frac{1}{C_{eq}} = \frac{1}{C_{1}} + \frac{1}{C_{2}}$

Capacitors in parallel combination,

$C_{eq} = C_{1} + C_{2}$

Step 3: Determining the equivalent capacitance of the combination

From Figure, it can be seen that, $C_{1}$ and $C_{2}$ are connected in parallel. Therefore,

From the equation 25-19, the equivalent capacitance is given by,

$C_{12} = C_{1} + C_{2}$

From the above figure, we can see that $C_{12}$ and $C_{3}$ are connected in a series.

From the equation 25-20, the equivalent capacitance is given by,

$\frac{1}{C_{eq}} = \frac{1}{C_{12}} + \frac{1}{C_{3}}$

Therefore,

$C_{eq} = \frac{C_{12} C_{3}}{C_{12} + C_{3}}$

Therefore,

$C_{eq} = \frac{(10.0 μF + 5.00 μF) \times 4.00 μF}{(10.0 μF + 5.00 μF) + 4.00 μF} C_{eq} = 3.16 μF$

Hence, the equivalent capacitance of the combination is 3.16 $μF$

Therefore, by using the formula of capacitors in series and parallel combinations, equivalent capacitance can be determined.

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Fundamentals Of Physics

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Short Answer

In Fig. 25-29, find the equivalent capacitance of the combination. Assume that $C_{1} = 10.0 μF$ , $C_{2} = 5.00 μF$ and $C_{3} = 4.00 μF$

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining the equivalent capacitance of the combination

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In Fig. 25-29, find the equivalent capacitance of the combination. Assume that C1=10.0μF, C2=5.00μF and C3=4.00μF

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining the equivalent capacitance of the combination

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In Fig. 25-29, find the equivalent capacitance of the combination. Assume that $C_{1} = 10.0 μF$ , $C_{2} = 5.00 μF$ and $C_{3} = 4.00 μF$