SATHEE: Electromagnetic Induction and Alternating Current 4 Question 1

Electromagnetic Induction and Alternating Current 4 Question 1

1. Consider the $L - R$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$ , then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is

(Main 2019, 12 April II)

(a) $\frac{2.7 E L}{R^{2}}$

(b) $\frac{E L}{2.7 R^{2}}$

(d) $\frac{E L}{7.3 R^{2}}$

Show Answer

Answer:

Correct Answer: 1. (b)

Solution:

In an $L - R$ circuit, current during charging is given by

$I = I_{0} 1 - e^{- \frac{R}{L} t}$

where, $I_{0} = \frac{E}{R} =$ saturation current

So, we have $\frac{d q}{d t} = I = I_{0} 1 - e^{- \frac{R}{L} t}$

$\Rightarrow d q = I_{0} 1 - e^{- \frac{R}{L} t} d t$

So, charge $q$ that passes through battery from time $t = 0$ to $t = \frac{L}{R}$ is obtained by integrating the above equation within the specified limits, i.e.

$\begin{aligned} q & = \int_{0}^{Q} d q = \int_{t = 0}^{t = \frac{L}{R}} I_{0} 1 - e^{- \frac{R}{L} t} d t \\ = I_{0} t - \frac{1}{- \frac{R}{L}} \cdot e^{- \frac{R}{L} t} \\ = \frac{E}{R} \frac{L}{R} + \frac{L}{R e^{'}} - 0 + \frac{L}{R} = \frac{E}{R} \times \frac{L}{R e} = \frac{E L}{R^{2} e} \\ \Rightarrow & q = \frac{E L}{2.7 R^{2}} \end{aligned}$

Electromagnetic Induction and Alternating Current 4 Question 1

1. Consider the $L - R$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$ , then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Electromagnetic Induction and Alternating Current 4 Question 1

1. Consider the L−R circuit shown in the figure. If the switch S is closed at t=0, then the amount of charge that passes through the battery between t=0 and t=LR is

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

1. Consider the $L - R$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$ , then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is