RLC Resonance: Understanding VL and VC Magnitudes

[Terocamo]

Homework Statement

The question ask if V_L=V_C if the circuit is under resonace

The Attempt at a Solution

I originally thought when resonance happens in RCL circuit, Vr=Vsupplied, therefore, by loops rule Vr+Vc+VL=Vsupplied, during reasonance Vr and Vsupplied canceled each other, so what's left is that Vc+VL=0. Thus, Vc= - VL instead of Vc=VL. Now that i see the official doesn't think that way so i am a little bit confused, is there anythink i thought wrong?

 

[rl.bhat]

Inductive reactance XL and capacitive reactance XC depends on the frequency. You have to consider phase difference between applied voltage and VC and VL. In the phase diagram XL and XC are in the opposite direction, So net impedance XL - XC. At resonance net impedance is zero. Hence VL - VC = 0.

 

[ehild]

They understand the magnitude (amplitude) or the rms value on VL and Vc, and those are what the meters read. The voltages on C and L are out of phase, but the magnitudes are the same.

ehild