Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

The current in a single-loop circuit with one resistance R is 5.0 A. When an additional resistance of 2.0 $Ω$ is inserted in series with R, the current drops to 4.0 A. What is R?

The value of R is.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

$I = 5.0 A R^{'} = 2.0 Ω I^{'} = 4.0 A$

Step 2: Determining the concept

Write for emf of the battery when the circuit has only resistance R and when R’ is inserted in the circuit using Ohm’s law. Equating them will give the value of R.

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

Formulae are as follow:

$I = \frac{V}{R}$

Where, I is current, V is voltage, R is resistance.

Step 3: Determining the value of R

Let the battery be emf V. Then, Ohm’s law gives,

$V = IR V = 5 R$

When R’ is inserted in the circuit in series with R, the total resistance of the circuit becomes R+R’.

Then emf is given by,

$V = I^{'} (R + R^{'}) V = 4 (R + 2)$

Equating the equations 1) and 2) gives,

$5 R = 4 R + 8 R = 8.0 Ω$

Hence, the value of R is $8.0 Ω$ .

Therefore, using Ohm’s law, the unknown resistance in the circuit can be found.

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Fundamentals Of Physics

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Short Answer

The current in a single-loop circuit with one resistance R is 5.0 A. When an additional resistance of 2.0 $Ω$ is inserted in series with R, the current drops to 4.0 A. What is R?

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining the value of R

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The current in a single-loop circuit with one resistance R is 5.0 A. When an additional resistance of 2.0 Ω is inserted in series with R, the current drops to 4.0 A. What is R?

Step by Step Solution

Step 1: Given

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The current in a single-loop circuit with one resistance R is 5.0 A. When an additional resistance of 2.0 $Ω$ is inserted in series with R, the current drops to 4.0 A. What is R?