Q. 105.0( 1 Vote )

# In a simple circuit of resistance R, self inductance L and voltage E, the current i at any time t is given by If E is constant and initially no current passes through the circuit, prove that

We know that in a circuit of R, L and E we have,

We can see that it is a linear differential equation of the form

Where P = and Q =

I.F = e∫Pdt

= edt

=

Solution of the given equation is given by

i × I.F = ∫Q × I.F dt + c

i × = ∫ × dt + c

i × = ∫ × dt + c

i = + c ……(1)

Initially, there was no current

So, at i = 0, t = 0

Now, putting the value of c in equation (1)

i =

i = (1 – )

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