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A coil of inductance 1.0 H and resistanc...

A coil of inductance 1.0 H and resistance 100 Omega is connected to a battery of emf 12 V. Find the energy stored in the magnetic field associated with the coil at an instant 10 ms after the circuit is switched on.

A

2.88 mJ

B

2.53 mJ

C

1.59 mJ

D

1.75 mJ

Text Solution

Verified by Experts

The correct Answer is:
A
L = 1.0 H R = `100Omega`
E = 12 V
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^(-(100xx 10xx 10^(-3))/(1)))^(2)`
=` (144)/(2xx 10^(4) (1 = (1)/(e))^(2) = 2.88 mJ`
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