Inductance of a coil in an AC L-R circuit

[ToxicBug]

Does the formula tan (phi) = (wL - 1/wC)/R work without a capacitor? Can I turn it into tan (phi) = wL/R instead? I don't know what formula to use to find the inductance of an inductor in this question:

A voltage source V = 160V sin (100t) is connected in series with an inductor and a 17.0 ohm resistor. The phase angle between the current and the voltage is 1.05 rad. Find:

a) the inductance of the coil, and
b) the average power consumption of a circuit.

 

[big man]

Does the formula tan (phi) = (wL - 1/wC)/R work without a capacitor? Can I turn it into tan (phi) = wL/R instead?

Yes you can. The only reason it is wL-1/wC is because when a capacitor is present it's phasor is in the opposite direction due to the opposite phase difference it produces. That is, an inductor's voltage leads the current by 90 degrees while the capacitor's voltage lags the current by 90 degrees.

 

[lightgrav]

Careful!
You're adding Voltages here, so the formula only applies if the LCR is in *series*!
Not having a break in the wire where the capacitor used to be means V=0 there.
Sometimes devices are placed in parallel, and the formula does not apply.

 

[big man]

yeah but he said it was in series.

 

[lightgrav]

I thought it would be helpful to give a couple of clues
as to why you don't set C=0 in that "formula".