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Q10Q

Expert-verifiedFound in: Page 894

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 ${\mathit{V}}{\mathit{R}}$ ****across a resistor in three circuits wired as shown in Fig. 30-16. The circuits contain the same resistance ${\mathit{R}}$**** and emf ${\mathit{\epsilon}}$**** but differ in the inductance L**

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

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

**Using Eq.30-41 and 30-42, predict the value of inductance L **

** **

Formulae are as follows:

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

$i=\frac{\epsilon}{R}\left(1\u2010{e}^{-t/{T}_{L}}\right)$

ii. The inductive time constant,

${T}_{L}=\frac{L}{R}$

From Eq.30-41, the current is,

$i=\frac{\epsilon}{R}\left(1\u2010{e}^{-t/{T}_{L}}\right)..................................................................................\left(30-41\right)$

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* 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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