AC Circuit Resonance Angular Frequency Calculation

In summary, in an L-R-C series circuit with L = 0.270 H and C = 3.80 µF, the resonance angular frequency can be found by setting the magnitude of the impedance to 0 and treating the inductance and capacitance as vectors. The voltage amplitude of the source is 120 V.
  • #1
steveironpump
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Homework Statement



In an L-R-C series circuit, L = 0.270 H and C = 3.80 µF. The voltage amplitude of the source is 120 V.
(a) What is the resonance angular frequency of the circuit?



Homework Equations



Xc = 1/(wC)

XL = wL

w=angular frequency

The Attempt at a Solution



I couldn't get anywhere. I know that I have to do something with the voltage, but I have no clue
 
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  • #2
Well you want the magnitude of the impedance to go to 0. And since they are both 180 degrees out of phase with each other and in series, you treat them like vectors and subtract them. Then solve for [tex]\omega[/tex].
 
  • #3
what to do next.



To calculate the resonance angular frequency of the circuit, we can use the formula w = 1/sqrt(LC), where L is the inductance and C is the capacitance. Plugging in the given values, we get w = 1/sqrt(0.270 H * 3.80 µF). This gives us a resonance angular frequency of approximately 1.70 x 10^4 rad/s. This means that at this frequency, the inductive reactance and capacitive reactance will cancel each other out, resulting in a maximum current and a minimum impedance in the circuit. This is known as resonance and is an important concept in AC circuits.
 

1. What is an AC circuit?

An AC (alternating current) circuit is a type of electrical circuit in which the current periodically changes direction. This is in contrast to a DC (direct current) circuit, where the current flows in only one direction.

2. How does an AC circuit differ from a DC circuit?

The main difference between an AC circuit and a DC circuit is the direction in which the current flows. In an AC circuit, the current periodically changes direction, while in a DC circuit, the current flows in only one direction. Additionally, AC circuits often use components such as capacitors and inductors, which are not commonly found in DC circuits.

3. What is the frequency of an AC circuit?

The frequency of an AC circuit is the number of times the current changes direction per second. It is measured in Hertz (Hz), with one Hz being equal to one cycle per second. The standard frequency for AC circuits in most countries is 50 or 60 Hz.

4. What is the difference between RMS and peak voltage in an AC circuit?

RMS (root mean square) voltage is a measure of the average voltage in an AC circuit over a full cycle. It takes into account the fact that the voltage in an AC circuit changes over time. Peak voltage, on the other hand, is the highest voltage reached in a cycle. For a sine wave, the RMS voltage is equal to the peak voltage divided by the square root of 2.

5. How does impedance affect an AC circuit?

Impedance is a measure of the opposition to current flow in an AC circuit. It is made up of both resistance and reactance, which is the opposition caused by components such as capacitors and inductors. In an AC circuit, impedance can affect the flow of current and the voltage across components, and is an important factor in determining the behavior of the circuit.

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