# Frequency & circuits

1. Jun 13, 2014

### jacksonwiley

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

For an RLC circuit with a resistance of 13.0 kΩ a capacitance of 7.0 µF, and an inductance of 35.0 H. What frequency is needed to minimize the impedance?
A) 0.064 kHz
B) 0.010 kHz
C) 12 kHz
D) 2.1 kHz

2. Relevant equations

Xc = 2∏ƒL
XL = 1/ (2∏ƒC)

3. The attempt at a solution

i'm really unsure if i need to use the XL or the Xc equation?
2(3.14)*frequency*L
or 1/(2(3.14)*frequency*capacitance
i've been stuck on this one forever.. any guidance is much appreciated!

2. Jun 13, 2014

### tms

Since the circuit has both inductive and capacitive reactance, you need to use both in your calculations.

3. Jun 13, 2014

### jacksonwiley

Would i just find the difference of the two?

4. Jun 13, 2014

### tms

You would use the total reactance, which is a function of $X_C$ and $X_L$. Then you have to do something with that equation to find the minimum.

5. Jun 13, 2014

### BiGyElLoWhAt

series circuit?

6. Jun 13, 2014

### jacksonwiley

Yeah I think it's assumed that this is a series RLC circuit

7. Jun 13, 2014

### jacksonwiley

if i set them equal to each other and then solved for frequency that would lead to the right answer, right?

8. Jun 14, 2014

### tms

Set what equal to what? There is an expression for the total reactance, given $X_C$ amd $X_L$; you need to use that. Once you get that, how do you find a minumum?

9. Jun 14, 2014

### Staff: Mentor

magnitudes of the reactances, yes.

10. Jun 14, 2014

### BiGyElLoWhAt

Are you measuring over the resistor?

11. Jun 14, 2014

### BiGyElLoWhAt

Also, I'm not sure if you can do this without considering the imaginary parts of the ractances. Maybe I'm wrong.

12. Jun 14, 2014

### BiGyElLoWhAt

Basically, yes. This comes from mapping out your transfer function and solving for the minimum reactance.

Try writing your total reactance as a function of $X_{c}$ & $X_{L}$.

But instead of using the equations you have, use $X_{c} = \frac{1}{i\omega c}$ & $X_{L} = IL\omega i$

with I being current, omega angular velocity, i the imaginary number, and L and c inductance and capacitance.

Or alternatively if you want to solve for frequency and not angular velocity you can later substitute $\omega = 2\pi f$

13. Jun 14, 2014

### CWatters

Perhaps try plotting or sketching the impedance of the L and C on a graph. Add a line for the sum. Find where it's a minimum.

or write an equation for the curve of the sum and then find it's minimum (eg where the slope is zero). Example

Last edited by a moderator: Sep 25, 2014