Solving Series RLC Circuit: Vrms Across Capacitor & Inductor is Zero

[reddawg]

Homework Statement

Given a series RLC circuit:

R = 10 Ω
L = 0.1 H
C = 2 μF
Power Source: V = 5sin(500t)

If you could change the capacitance what C would you select so V_rms across the capacitor and inductor is zero?

Homework Equations

ω² = 1/LC

The Attempt at a Solution

My instructor's solutions say to use above equation for resonance frequency to input ω=500 (given from V) and
L = 0.1 H and then solve for C, yielding 0.00004 F.

This makes no sense, could someone explain it to me?

 

[Svein]

This makes no sense, could someone explain it to me?

Remember: The voltage across the inductance is 180° out of phase with respect to the voltage across the capacitor (jωL vs. 1/[jωC]).

 

[reddawg]

Remember: The voltage across the inductance is 180° out of phase with respect to the voltage across the capacitor (jωL vs. 1/[jωC]).

Ok, I think I get it.

Given a phaser representation, tan(φ) = (X_L - X_C) / R

So tan(180) = 0 ⇒ X_L = X_C which is resonance.