Current & Voltage Relationship in LCR Series Circuit

[physicsprasanna]

the question is :
suppose the resonance frequency of the LCR series circuit is fr. Will the current in the circuit lag behind the voltage or lead the voltage in the following cases :
(i) when the applied AC frequency f > fr
(ii) when f < fr

we can say that the current lags behind the voltage when the circuit in inductive. The phase angle can be calculated by $$\tan\phi=\frac{X_{L}-X_{C}}{R}$$ . But how can we conclude whether XL - XC is positive or not when we are given the applied frequency.

I was able to figure out one thing. When the applied frequency is same as the resonance frequency, XL = XC , which means $$\tan\phi=0$$. so the current and voltage are in phase.

 

[topsquark]

the question is :
suppose the resonance frequency of the LCR series circuit is fr. Will the current in the circuit lag behind the voltage or lead the voltage in the following cases :
(i) when the applied AC frequency f > fr
(ii) when f < fr

we can say that the current lags behind the voltage when the circuit in inductive. The phase angle can be calculated by $$\tan\phi=\frac{X_{L}-X_{C}}{R}$$ . But how can we conclude whether XL - XC is positive or not when we are given the applied frequency.

I was able to figure out one thing. When the applied frequency is same as the resonance frequency, XL = XC , which means $$\tan\phi=0$$. so the current and voltage are in phase.

What you need to do here is sketch a quick phasor diagram of the circuit. The details don't matter, just as long as you have something to work with. Now, both $$X_C$$ and $$X_L$$ depend on the frequency of the current in the circuit. So what happens to $$X_C$$ as we increase the frequency from the resonance frequency? What happens to $$X_C$$ as we increase the frequency from resonance frequency? What do these changes do to your phasor diagram? From this you can figure out what happens to your phase angle.

-Dan