Question

For the circuit shown in figureure, find the instaneous current through each element.
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Answer 1

The three current equations are,
`V=I_(R)R, V=L(dI)_(L))/(dt)` and `(dV)/(dt) = 1/CI_(C)`.............(i)
The steady state solutions of Eq. (i) are, `I_(R) = V_(0)/Rsinomegat-=(I_(0))_(R)sinomegat`
`I_(L) = -V_(0)/(omegaL) cosomegat=V_(0)/X_(L)cosomegat-=-(I_(0))_(L)cosomegat`
and `I_(C)=V_(0)omegaCcosomegat =V_(0)/X_(C) cosomegat-=(I_(0))_(C) cosomegat`............(ii)
where, the reactance `X_(L)` and `X_(C)` are as defined.