# Homework Help: Question on Harmonics

1. Oct 30, 2014

### Cartman

A serie RLC Circuit consists of 20ohm Resistor, an inductor with an inductance of 130mH and a variable capacitor. The capacitor is set to give resonance to the circuit at the third harmonic. The instantaneous value of the sinusoidal voltage across the circuit is represented by
v(t) = 78 + 120sin251t + 84sin(753t+ pi/5) + 72sin(1255t + pi/4) volts

1.Calculate the iductive reactance at the fundemanetal and 3rd harmonic.
2.Deteremine an expression for the current drawn from the supply
3.Calculate overall power factor of the circuit.

Now I dont get how they can ask to get the 3rd harmonic. DO I take 120sin251t as the Third harmonic? which one do I use?

So far Ive gathered that the Fundamental Harmonic would be 120Sin251t and to get its inductive Reactance I would multiply the 251*(0.000130) to het the Reactance of the Inductor for the FIRST Harmonic. What baffles me is that theres a CAPACITOR involved? How would that work?

Last edited: Oct 30, 2014
2. Oct 30, 2014

### Staff: Mentor

Are you sure the word "sinusoidal" is used here in the problem statement?

The sin (753t) term would be the third harmonic.

It's a series circuit, so you add the impedances of all 3 elements at the frequency under consideration. Add using phasor addition.

The capacitor is present to form a resonance at the frequency where it cancels the inductor's impedance. At frequencies away from resonance the capacitor just adds some series impedance.

3. Oct 31, 2014

### rude man

You were given L = 130 mH which is 0.130 Hy.