Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Figure 30-30 gives the variation with time of the potential difference $V R$ across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance $R$ and emf $ε$ but differ in the inductance L . Rank the circuits according to the value of L , greatest first.

The ranks of the given circuit according to the value of L are 1) c, 2) b, and 3) a.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Fig.30-30.
Fig.30-16.
All the circuits contain the same resistor R and emf $ε$ .
All the circuits contain different inductances L .

Step 2: Determining the concept

Using Eq.30-41 and 30-42, predict the value of inductance L from potential difference V_R vs time t ; that is from Fig.30-30. From the value L , find the ranks of the given circuit.

Formulae are as follows:

i. From Eq.30-41, the current is,

$i = \frac{ε}{R} (1 ‐ e^{- t / T_{L}})$

ii. The inductive time constant,

$T_{L} = \frac{L}{R}$

Step 3: Determining the ranks of the given circuit according to the value of L

From Eq.30-41, the current is,

$i = \frac{ε}{R} (1 ‐ e^{- t / T_{L}}) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30 - 41)$

Where, the inductive time constant is given by,

$T_{L} = \frac{L}{R} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (30 - 42)$

From Eq.30-42, the higher value of inductance L causes the potential difference V_R across the resistance R to take more time to reach its maximum and the lower value of inductance L causes the potential difference V_R across the resistance R to take less time to reach its maximum.

From Fig.30-30, curve a gives the potential difference V_R takes less time to reach its maximum as compared to that in curve b, and also, curve b gives the potential difference V_R takes less time to reach its maximum as compared to that curve c. Therefore, the value of inductance L is more in curve c as compared with that in curve b and also the value of inductance L is more in curve b as compared with that in curve a.

Therefore, the ranks of the given circuit according to the value of L are c, b, and a.

Using Eq.30-41 and 30-42, and applying the properties of RL circuits, answer this question.

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Fundamentals Of Physics

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Short Answer

Figure 30-30 gives the variation with time of the potential difference $V R$ across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance $R$ and emf $ε$ but differ in the inductance L . Rank the circuits according to the value of L , greatest first.

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining the ranks of the given circuit according to the value of L

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Figure 30-30 gives the variation with time of the potential difference VR across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance R and emf ε but differ in the inductance L . Rank the circuits according to the value of L , greatest first.

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: Determining the ranks of the given circuit according to the value of L

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Figure 30-30 gives the variation with time of the potential difference $V R$ across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance $R$ and emf $ε$ but differ in the inductance L . Rank the circuits according to the value of L , greatest first.