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In the figure below, the switches S_{1} and S_{2} are closed s

Question

Hard

Solving time: 4 mins

In the figure below, the switches $S_{1}$ and $S_{2}$ are closed simultaneously at $t = 0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{m a x}$ at time $t = τ$ . Which of the following statements is (are) true?

SELECT MULTIPLE OPTION

I_{max} = \frac{V}{2 R}

I_{m a x} = \frac{V}{4 R}

τ = \frac{L}{R} ln 2

τ = \frac{2 L}{R} ln 2

Views: 6,367 students

Updated on: May 7, 2023

Book:

Electricity and Magnetism (DC Pandey)

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Owen Discussed

In the figure below, the switches

S_{1}

and

S_{2}

are closed simultaneously at

t = 0

and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current

I

in the middle wire reaches its maximum magnitude

I_{m a x}

at time

t = τ

. Which of the following statements is (are) true?

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

(b, d)

I_{1} = \frac{V}{R} (1 - e^{- \frac{tR}{L}})

I_{2} = \frac{V}{R} (1 - e^{- \frac{tR}{2 L}})

From principle of superposition,

I \Rightarrow I = I_{1} - I_{2} = \frac{V}{R} e^{- \frac{tR}{2 L}} (1 - e^{- \frac{tR}{2 L}})

I

is maximum when

\frac{d l}{d t} = 0

, which gives

e^{- \frac{tR}{2 L}} = \frac{1}{2}

t = \frac{2 L}{R} ln 2

Substituting this time in Eq. (i), we get

I_{m a x} = \frac{V}{4 R}

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Question Text	In the figure below, the switches $S_{1}$ and $S_{2}$ are closed simultaneously at $t = 0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{m a x}$ at time $t = τ$ . Which of the following statements is (are) true?
Updated On	May 7, 2023
Topic	Electromagnetic Induction
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 4
Upvotes	415
Avg. Video Duration	7 min

Text solutionVerified

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