- #1

cnh1995

Homework Helper

Gold Member

- 3,448

- 1,148

## Homework Statement

## Homework Equations

Kirchhoff's laws

## The Attempt at a Solution

Applying KVL on primary,

di

_{1}/dt+i

_{1}=5+2di

_{2}/dt.....1)

Similarly for secondary,

2di

_{1}/dt= 4di

_{2}/dt + i

_{2}.....2)

After solving these equations using Laplace Transform, I got

I

_{1}= 5-e

^{-0.2t}A and

I

_{2}= 2e

^{-0.2t}-2e

^{-0.25t}.

I have verified these answers using initial and final conditions and I believe they are correct.

However, at t=0, the energy in the system comes out to be 8J (E= 0.5L

_{1}i

_{1}

^{2}+0.5L

_{2}I

_{2}

^{2}-Mi

_{1}i

_{2}, since there is magnetic opposition).

How is this possible? How can the energy change instantaneously here?

For E to be zero at t=0, i

_{2}at t=0 should be 2A. But here, i

_{2}|

_{t=0}= 0A.

What am I missing here?