Solving RLC Circuit w/ 3rd Harmonic - Question on Harmonics

[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 don't 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 I've 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 there's a CAPACITOR involved? How would that work?

 

[NascentOxygen]

The instantaneous value of the sinusoidal voltage across the circuit is

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.

 

[rude man]

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.

So far I've 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.

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