Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?

The value of the direct current is 1.84 A.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Listing the given quantities:

The current, $i = 2.60 A$

Step 2: Understanding the concepts of power dissipation:

Average power dissipated in resistance R when the current is AC and DC should be equated to find the direct current which will produce the same amount of thermal energy as an alternating current of 2.60 A

Formula:

Power Dissipation, $P_{d} = i_{d}^{2} R$

Step 3: Calculation of the value of the direct current:

Average power dissipated in resistance R when current is AC.

$P_{avg} = i_{rms}^{2} R$

The power is dissipated in resistor R when current is DC.

$P_{d} = i_{d}^{2} R$

Both these powers produce the same thermal energy. Hence,

$\begin{array}{rcl} P_{avg} & = & P_{d} \\ i_{rms}^{2} R & = & i_{d}^{2} R \\ i_{d} & = & i_{rms} \\ = & \frac{i}{\sqrt{2}} \end{array}$

Substitute 2.60A for i in the above equation.

$\begin{array}{rcl} i_{d} & = & \frac{i}{\sqrt{2}} \\ = & \frac{2.6}{\sqrt{2}} \\ = & 1.84 A \end{array}$

Hence, the value of the direct current is 1.84A.

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Fundamentals Of Physics

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Short Answer

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?

Step by Step Solution

Step 1: Listing the given quantities:

Step 2: Understanding the concepts of power dissipation:

Step 3: Calculation of the value of the direct current:

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Fundamentals Of Physics

Answers without the blur.

Short Answer

What direct current will produce the same amount of thermal energy, in a particular resistor, as an alternating current that has a maximum value of 2.60 A?

Step by Step Solution

Step 1: Listing the given quantities:

Step 2: Understanding the concepts of power dissipation:

Step 3: Calculation of the value of the direct current:

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