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 postive 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 postive 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

 

[kyle8921]

To determine whether XL - XC is positive or negative, we can use the equation XL - XC = 2π(fL - 1/fC), where L is the inductance and C is the capacitance of the circuit. If f > fr, then XL > XC and the phase angle will be positive, indicating that the current lags behind the voltage. Conversely, if f < fr, then XL < XC and the phase angle will be negative, indicating that the current leads the voltage.

This relationship between current and voltage in an LCR series circuit is due to the properties of inductors and capacitors. Inductors store energy in the form of a magnetic field, which resists changes in current. This causes the current to lag behind the voltage. On the other hand, capacitors store energy in the form of an electric field, which resists changes in voltage. This causes the current to lead the voltage.

In summary, the current in an LCR series circuit will lag behind the voltage when the applied frequency is greater than the resonance frequency, and will lead the voltage when the applied frequency is less than the resonance frequency. This is due to the properties of inductors and capacitors and can be determined by comparing the reactance of the inductor and capacitor at the given frequency.