RLC Resonance: Understanding VL and VC Magnitudes

In summary, the conversation discusses the question of whether VL is equal to VC in a circuit under resonance. The Attempt at a Solution presents a different thought process from the official solution, which considers the phase difference between applied voltage and VC and VL. The conversation also mentions that the magnitudes of VL and VC are the same, but they are out of phase.
  • #1
Terocamo
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0

Homework Statement


The question ask if VL=VC 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?
 

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  • #2
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.
 
  • #3
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
 

Related to RLC Resonance: Understanding VL and VC Magnitudes

1. What is RLC resonance?

RLC resonance is a phenomenon that occurs when a circuit consists of a resistor (R), inductor (L), and capacitor (C) connected in series or parallel. When the frequency of the applied voltage matches the resonant frequency of the circuit, the impedance of the circuit is at its minimum and the voltage across the inductor and capacitor are equal.

2. How is resonance achieved in an RLC circuit?

Resonance is achieved in an RLC circuit when the frequency of the applied voltage is equal to the resonant frequency of the circuit, which is determined by the values of the inductance and capacitance. At resonance, the reactance of the inductor and capacitor cancel each other out, resulting in a minimum impedance and maximum current flow.

3. What is the formula for calculating the resonant frequency in an RLC circuit?

The formula for calculating the resonant frequency in an RLC circuit is f0 = 1 / (2π√(LC)), where f0 is the resonant frequency, L is the inductance in henries, and C is the capacitance in farads.

4. Does the voltage across the inductor (VL) equal the voltage across the capacitor (VC) in resonance?

Yes, in resonance, the voltage across the inductor and capacitor are equal. This is due to the fact that at resonance, the reactance of the inductor and capacitor cancel each other out, resulting in a voltage drop across each component that is equal in magnitude.

5. How does RLC resonance affect the current in the circuit?

At resonance, the impedance of the circuit is at its minimum, resulting in a maximum current flow. This means that in an RLC circuit, the current will be at its highest when the frequency of the applied voltage is equal to the resonant frequency of the circuit.

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