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Expert-verified Found in: Page 894 ### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718 # Figure 30-30 gives the variation with time of the potential difference ${\mathbit{V}}{\mathbit{R}}$ across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance ${\mathbit{R}}$ and emf ${\mathbit{\epsilon }}$ 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.

See the step by step solution

## Step 1: Given

1. Fig.30-30.
2. Fig.30-16.
3. All the circuits contain the same resistor R and emf $\epsilon$ .
4. 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 VR 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,

$i=\frac{\epsilon }{R}\left(1‐{e}^{-t/{T}_{L}}\right)$

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,

$i=\frac{\epsilon }{R}\left(1‐{e}^{-t/{T}_{L}}\right)..................................................................................\left(30-41\right)$

Where, the inductive time constant is given by,

${T}_{L}=\frac{L}{R}..................................................................................................\left(30-42\right)$

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

From Fig.30-30, curve a gives the potential difference VR takes less time to reach its maximum as compared to that in curve b, and also, curve b gives the potential difference VR 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. ### Want to see more solutions like these? 