- #1

- 101

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_{0}sinωt, converted into the above via a Norton equivalent).

I have obtained I

_{L}=V

_{0}sinωt/R[1+i(ωL/R)-(ω

^{2}LC)] by first finding the common voltage across each component.

The problem then says that the circuit is excited at the resonant frequency ω

_{0}=1/√LC by a voltage cosω

_{0}t. I need to calculate I

_{L}(t). This reduces my expression to I

_{L}=cosω

_{0}t/iω

_{0}L.

Now I need to get this to be real. I just wrote cosω

_{0}t=e

^{iω0t}and i=e

^{iπ/2}giving I

_{L}=cos(ω

_{0}t-π/2)/ω

_{0}L after taking the real part.

Now I'm not sure if this is correct. Besides that, if it is, I don't quite understand why I would be allowed to do that. Why would I just take the real part at the end. It just doesn't seem mathematiclly rigorous and so if somebody could explain the maths behind the approach I would feel more comfortable. Thanks.