Solving a Series LRC Circuit with Complex Impedances

[nateja]

Homework Statement

A series L-R-C circuit consisting of a voltage source, a capacitor of capacitance , an inductor of inductance , and a resistor of resistance is driven with an AC voltage of amplitude and frequency . Define to be the amplitude of the voltage across the resistor and the inductor.

FIND THE ratio Vout/Vin

picture: http://www.chegg.com/homework-help/questions-and-answers/series-l-r-c-circuit-consisting-voltage-source-acapacitor-capacitance-inductor-inductance--q416667?frbt=1

Homework Equations

Z = sqrt((IR)^2+(I*X_L-I*X_C)^2)

The Attempt at a Solution

I found Vin = sqrt((IR)^2+(I*X_L-I*X_C)^2)

Then I googled the question for Vout and tried to use kirchhoffs voltage and loop rule. I only found solutions using laplace transforms or something - I am in calc 2.

Any kind of hint in the right direction would be nice. I don't understand the 'dot' notation on the circuit. And the whole problem is really throwing me in circles.

 

[cepheid]

In a circuit, open circles are usually used to represent points (terminals) at which you measure a voltage. In this case, they've used closed circles instead, and they're just indicating that Vout is the voltage measured between these two terminals.

That's all the dots are.

 

[cepheid]

You don't need to use Laplace transforms. You can just use KVL and solve the circuit normally, except that you need to use the impedance of each component which, in general, is a complex number.

What is the expression for the impedance of an inductor? How about a capacitor?

Since this is a series circuit, what is the current in terms of the source voltage and the impedances?