the current flowing through an inductor of self-inductance L is continuously increasing. plot a graph showing the variation of
1) magnetic flux versus current.
2)induced emf versus dI/dt.
3)magnetic potential energy versus the current
please explain in detail and clearly 

Asked by modi72879 | 21st Nov, 2017, 04:58: PM

Expert Answer:

The basic equation related to inductance and induced emf is given by
begin mathsize 12px style negative e space equals space L space fraction numerator d i over denominator d t end fraction....................... left parenthesis 1 right parenthesis end style
L is inductance, e is induced emf, I is current and t is time.

Faraday's law that relates induced emf and rate of change of magnetic flux through N turns of coil is given by
 
begin mathsize 12px style e space equals space minus space N fraction numerator d ϕ over denominator d t end fraction................................ left parenthesis 2 right parenthesis end style
From the above equations (1) and (2) we can write,
begin mathsize 12px style integral L d i space equals space integral N d ϕ L cross times i space equals space N cross times ϕ space ϕ equals space L over N i end style
(1) Hence the graph for variation of magnetic flux against current is linear
 
(2) the graph for the variation of induced emf versus di/dt lso linear as per the equation (1) given here.
 
The current flowing in the inductance has to do work against the induced emf in the inductance. This work is stored as magnetic potential energy in the inductor.
The work done is given by

begin mathsize 12px style d w space equals space P cross times d t space equals space epsilon cross times i cross times d t space equals space L cross times i cross times d i  integral d w space equals space w space equals space integral L i d i space equals space 1 half L i squared end style
 
(3) Hence the magnetic potential energy proportional to square of current
 
The required graphs are shown below


 

 


Answered by  | 27th Nov, 2017, 03:48: PM

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