Question

What is the Norton equivalent current source at terminal a-a' for the circuit (see attachment below),for t>0.Initial conditions are shown at t=0 ?

Answer 1

2 amps is the current source and open circuit impedance is 2 ohms

Answer 2

I need expression or formula .

Answer 3

I never saw Norton being used in a not purely resistive circuit so I'm not sure about what approach to take. I can't consider the capacitor a simple constant battery nor the inductor something with no resistance as it would in constant current. So maybe this circuit is to be interpreted as being in resonance. Taking that approach I see the capacitor as a constant battery and a resistance, and the inductor as resistance. Both calculated using the resonance frequency and their capacitance/inductance. After this I have a very pretty resistive circuit easy to calculate the Norton equivalent. But there is a final leap that I'm not sure about. After I calculated the impedance I calculated the equivalent resistance of the circuit as if it were a simple resistance, what they are not strictly speaking. The final result I found was ~2,9A and ~0,7ohms. I'm really insecure about this answer but maybe it can at least start a discussion about the behaviour assumptions I made.