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Question

A coil of inductance 1 henry and resistance 10Ω is connected to an ideal battery of emf 50 V at time t=0. Calculate the ratio of the rate at which magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at t=0.1 sec.

A
e
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B
1e1
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C
11e
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D
1e
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Solution

The correct option is D 1e
D. 1e
Given,
L=1H
R=10Ω
V0=50V
t=0.1sec
The current in LR circuit.
I=I0(1et/τ). . . . . .(1 )
where, τ=LR
τ=110=0.1sec
The rate at which magnetic energy is stored in the coil,
K=dEdt=d(12LI2)dt
K=dEdt=250(e1e2) by putting the value of I at t=0.1sec. . . . . . .(2)
The energy supplied by battery,
E=V0It
E=250(e1e) By puttting the value of I at t=0.1sec. . . . . .(3)
Dividing euation (2) by (1), we get
KE=1e
Thus, the correct option D


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