Impulse function applied to RLC circuit

[marc.orr]

Hello, I've been reviewing some material from my undergraduate studies. In the book "Signals and Systems" by Haykin in the first chapter he gives an example of a voltage source with the value of Vo*delta(t) applied to a series RLC circuit.

Vo is some arbitrary constant and delta(t) is the impulse function. The question is what is the value of the current i(t) at time t=0+ where 0+ is at 0 looking from the more positive side of time.

He says the answer is (without any sort of derivation) Io = Vo/L. How is this possible? I figure that as there is an instantaneous change in voltage, the inductor will look like a short circuit and the capacitor will look like an open circuit. So how can there be any current flow?

Thankyou in advance.

Marc

 

[NoTime]

I figure that as there is an instantaneous change in voltage, the inductor will look like a short circuit and the capacitor will look like an open circuit.

You have this reversed.

 

[SGT]

If you write the differential equation and integrate it between 0- and 0+ you can find Io.