The current in a coil of self inductance \(2.0\ H\) is increasing according to \(I = 2\ sin(t^2)\ A\). The amount of energy spent during the period when current changes from 0 to \(2\ A\) is _______ \(J\).
Correct Answer: 4
Solution and Explanation
The amount of energy,
\(U = \frac 12LI^2\)
\( U = \frac 12\times 2\times 2^2\)
\(U = 4\ J\)
So, the answer is \(4\ J\).
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Concepts Used:
Electromagnetic Induction
Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field.
- When the conductor constantly moves in a stationary field.
Formula:
The electromagnetic induction is mathematically represented as:-
e=N × d∅.dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
- t = time
Applications of Electromagnetic Induction
- Electromagnetic induction in AC generator
- Electrical Transformers
- Magnetic Flow Meter