Electromagnetic Induction and Alternating Current 4 Question 11

####11. In the figure below, the switches S1 and S2 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 Imax at time t=τ. Which of the following statements is (are) true?

(2018 Adv.)

(a) Imax=V2R

(b) Imax=V4R

(c) τ=LRln2

(d) τ=2LRln2

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Answer:

Correct Answer: 11. (b, d)

Solution:

I1=VR1etRL

From principle of superposition,

I=I1I2I=VRetR2L1etR2L

I is maximum when dIdt=0, which gives

etR2L=12 or t=2LRln2

Substituting this time in Eq. (i), we get Imax=V4R



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