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A coil of inductance 1.0 H and resistanc...

A coil of inductance 1.0 H and resistance 100 `ohm` is connected to a battery of emf 12 V. Find the energy stored in the magnetic field of the coil 10 ms after the circuit is switched on.

A

2.88mJ

B

2.53mJ

C

1.58mJ

D

1.75mJ

Text Solution

Verified by Experts

The correct Answer is:
A
`L= 1.0H R= 100Omega`
E= 12V
`i(t) = (E )/(R ) (1- e^(-(Rt)/(L)))`
Energy stored in the magnetic field is `(1)/(2) Li^(2)`
`=(1)/(2) xx 1.0 xx ((12)^(2))/(10^(4)) (1-e^(-(100 xx 10 xx 10^(-3))/(1)))^(2)`
`=(144)/(2 xx 10^(4)) (1-(1)/(e ))^(2) = 2.88mJ`
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