# What is the dependence of current through inductor in parallel RLC CIRCUIT with a AC source at resonance frequency

Consider the parallel RLC circuit: simulate this circuit – Schematic created using CircuitLab

Assuming $$C,L> 0$$ $$I(t) = U(t)*cos(t/(LC)^{0.5})$$ So, we have a source that starts working at t=0 at the resonant frequency. I'm being asked about 2 possible conditions:

1. The initial current through the inductor is 0 and the initial voltage across the capacitor is zero.

2. The initial current through the inductor is GREATER than zero and the voltage across the capacitor is equal to 1/R.

In which condition the current through the inductor approaches infinity and how can you explain that physically?

I have found the general solutions to both of these problems:

1. For the first option I get a blocked sin function, so in this case the current does not approach infinity as times goes by.

2. For the second option I get an exponent with a positive power so the current does approach infinity as time goes by.

But how can I explain that physically? I mean, in both cases the source works at the resonant frequency and all that is changing are the initial conditions.

Can anyone please clarify for me what does the initial values of the capacitor and the inductor have to do with the current?

• "the initial capacitance in the capacitor is zero" - do you mean current is zero? Jul 3 '14 at 10:36
• ohhh sorry mate, i meant voltage across the capacitor. fixed Jul 3 '14 at 10:41
• I also assume you meant R to be positive Jul 3 '14 at 10:52