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## Homework Statement

A resistor (R), capacitor (C), and inductor (L) are connected in series. What is the complex impedance, Z,

of this LCR series combination?

An AC supply of voltage V(t)=V

_{0}

*e*

^{iωt}is applied across an LCR series combination.

Derive an expression for the current I(t) in the circuit. From your expression for I(t)

write down expressions for both the magnitude of the current and the tangent of the

phase angle between current and applied voltage.

## Homework Equations

Z

Z

Z

I(t)=V(t)/Z.

_{L}=iωLZ

_{C}=-i/(ωC)Z

_{R}=RI(t)=V(t)/Z.

where; ω=Angular frequency of the voltage and i=√(-1).

## The Attempt at a Solution

For the total impedance I got:

Z=R+i(ωL-[itex]\frac{1}{ωC}[/itex]),

and for the current:

I=(V

_{0}*e*^{iωt})/(R+i(ωL-[itex]\frac{1}{ωC}[/itex])).For the tangent of the phase angle it would just be the tangent of the argument of the above equation for the current? If so, I can't get it into a "nice" equation without a trig function of another trig function. Thank you for any help.

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