# A tricky one...

by smunger81
Tags: tricky
 P: 254 Well you don't have a capacitor in your circuit to start off with so you don't actually need to know it, nor does it appear in the impedance expression. It usually helps to construct phasor diagrams in this situation. If you construct a phasor diagram you can see that the phase angle $$\phi$$ between the current and voltage is related by the expression: tan($$\phi$$) = $$X_L/R$$ From this you can express $$X_L$$ in terms of R or R in terms of $$X_L$$ and then solve the original impedance expression of: $$Z^2$$ = $$R^2$$ +$$X_L^2$$
 P: 254 A tricky one... Yeah the only reason it is $$X_L-X_C$$ for the impedance in an RLC series circuit is because the voltage across the inductor leads the current by 90 degrees while the voltage across the capacitor lags the current by 90 degrees. But phasors sometimes help to make these questions a lot easier.