
There is an inductor of . Current flowing through the inductor at any instant of time is given by the relation.
If, is in ampere and in sec, find out
(i) Emf induced in the inductor at and .
(ii) Plot graph.
Answer
141k+ views
Hint: Use the formula of the emf given below and substitute the value of the induction and the equation of the current. Differentiate the current equation, and substitute the value of the time taken in it to find the emf at that corresponding time. The emf is directly proportional to time taken.
Useful formula:
The formula of the emf is given by
Where is the emf of the inductor, is the induction and is the current flowing through the inductor circuit.
Complete step by step solution:
It is given that the
The inductance of the inductor,
The current through the inductor at time,
(i) Let us calculate the value of the emf through the inductor at . First, write the formula of the emf,
Substitute the known values in the above step,
By performing differentiation in the above step,
-----(1)
Substituting the value of as ,
Let us calculate the emf for ,by substituting the value of as ,
Hence the emf of the inductor is obtained as for time and for the time period of .
(ii) The below graph shows the relation between the emf and the time taken for the current to flow. The emf is directly proportional to the current and thus the graph is straight line.

Note: The inductors can be functioned in two ways, first is to control signals and in the other is to store electrical energy. In the factor that helps to produce the emf, also generate the reactive fluxes that act against the produced emf.
Useful formula:
The formula of the emf is given by
Where
Complete step by step solution:
It is given that the
The inductance of the inductor,
The current through the inductor at time,
(i) Let us calculate the value of the emf through the inductor at
Substitute the known values in the above step,
By performing differentiation in the above step,
Substituting the value of
Let us calculate the emf for
Hence the emf of the inductor is obtained as
(ii) The below graph shows the relation between the emf and the time taken for the current to flow. The emf is directly proportional to the current and thus the graph is straight line.

Note: The inductors can be functioned in two ways, first is to control signals and in the other is to store electrical energy. In the factor that helps to produce the emf, also generate the reactive fluxes that act against the produced emf.
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