# Homework Help: LRC Series Circuit Voltage amplitude question.

1. Dec 7, 2014

### BrettJimison

1. The problem statement, all variables and given/known data
Hello All,

I have a question:
In a LRC Series circuit:

At what angular frequency is the voltage amplitude across the resistor at a maximum value?
At what angular frequency is the voltage amplitude across the inductor at a maximum value?

2. Relevant equations

$$\omega = \sqrt{(\frac{1}{LC})-(\frac{R^{2}}{4L^{2}})}$$

3. The attempt at a solution

Im just looking for some assurance.

Do I simply just solve the equation for R ( for the first question) and optimize the function?

(And then just Solve the eqn for L for the second question and do the same?)

Seems to simple and my book has this as a Level III problem.

2. Dec 7, 2014

### BrettJimison

Actually I left one part out:

How do I find voltage amplitude? I know I will optimize a function somewhere but I'm not sure which one.....

3. Dec 7, 2014

### Staff: Mentor

If you work with impedance values (complex form of "resistance") for the components, then you can write the expressions for the various voltages as voltage divider equations. You might also ponder how the impedance of the various components vary with frequency.

4. Dec 7, 2014

5. Dec 7, 2014

### BrettJimison

I got it, thanks though!

I would explain how but it requires A LOT of steps. The derivative for d(Vl)/d(omega) is really nasty.

for a I got: $$\omega =\frac{1}{\sqrt{LC}}$$

for b I got: $$\omega = \frac{1}{\sqrt{LC-\frac{(RC)^{2}}{2}}}$$

Part a was easy, part b required me to take the derivative of V L (voltage amplitude across inductor) with respect to omega.

The function I derived was: $$V_{L}= \frac{VL\omega}{\sqrt{R^{2}+(\omega L-\frac{1}{\omega C})^{2}}}$$

too much latex to show, but in the end ,

$$\frac{dV_{L}}{d\omega }=0$$ when $$\omega = \frac{1}{\sqrt{LC-\frac{(RC)^{2}}{2}}}$$ in the end.

....In case anyone was interested..