The figure shows the plot of magnitude of induced emf ( ) versus the rate of change of current in two coils ‘1’ and ‘2’. Which coil has a greater value of self-inductance and why?
Official Solution
Correct Option:
(1)
The induced electromotive force (emf) in a coil is related to the rate of change of current through the coil by Faraday's law of induction, which is given by:
where:
- is the induced emf,
- is the self-inductance of the coil,
- is the rate of change of current. From this equation, we see that the induced emf ( ) is directly proportional to the rate of change of current ( ) and the self-inductance of the coil. Therefore, the coil with the steeper slope in the plot will have a greater value of self-inductance. Analyzing the Plot:
- In the plot, coil 1 has a steeper slope than coil 2, which means that for the same rate of change of current ( ), coil 1 produces a larger induced emf.
- According to the relationship , a larger induced emf for the same rate of change of current implies a larger value of self-inductance. Thus, coil 1 has a greater value of self-inductance than coil 2.
About Faraday S Law - CBSE-CLASS-XII
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