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

In summary, when given a series RLC circuit with specific values for R, L, and C, and a power source of V = 5sin(500t), the goal is to find a value for capacitance (C) that will make the root mean square (Vrms) voltage across the capacitor and inductor zero. To do this, we can use the equation ω^2 = 1/LC to calculate the resonance frequency (ω) and then input this value into the equation tan(φ) = (XL - XC)/R, where tan(φ) = 180° and XL = XC. This will result in a value of C that will make the Vrms across the capacitor and inductor zero
  • #1
reddawg
46
0

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 Vrms 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?
 
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  • #2
reddawg said:
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]).
 
  • #3
Svein said:
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) = (XL - XC) / R

So tan(180) = 0 ⇒ XL = XC which is resonance.
 

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

What is a Series RLC Circuit?

A Series RLC Circuit is a circuit that contains a resistor, inductor, and capacitor connected in series. This means that the components are connected one after the other, with the same current flowing through each component.

Why is the Vrms Across the Capacitor and Inductor Zero?

The Vrms (Root Mean Square Voltage) across the capacitor and inductor is zero because they are in series and have equal and opposite reactances. This results in a cancellation of voltage across the components, resulting in a net voltage of zero.

What is the significance of Vrms being Zero?

The Vrms being zero in a Series RLC Circuit indicates that the circuit is in a state of resonance. This means that the circuit is at its natural frequency and the energy is being exchanged between the inductor and capacitor without any net energy loss.

How do I solve for Vrms in a Series RLC Circuit?

To solve for Vrms in a Series RLC Circuit, you can use the formula Vrms = Vmax / √2, where Vmax is the maximum voltage across the circuit. You can also use Ohm's Law (V = IR) to calculate the voltage across each component and then use the Pythagorean theorem to find the net voltage.

What are some real-world applications of Series RLC Circuits?

Series RLC Circuits are commonly used in electronic filters, such as audio filters, to select specific frequencies and remove unwanted frequencies. They are also used in radio frequency circuits and power supplies to regulate voltage. Series RLC Circuits are also used in resonance imaging machines in the medical field.

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