RLC Circuit- Find average power in circuit

In summary, when the power factor of an RLC circuit is equal to one, the phase angle between the maximum voltage and current is zero. This means that the inductive reactance and capacitive reactance are equal. By knowing the values of these reactances at the resonant frequency, the inductance and capacitance of the circuit can be calculated. At a different frequency, the impedance can be found using the values of inductance, capacitance, and resistance. The phase angle between voltage and current can then be calculated and used to find the average power of the circuit.
  • #1
yankeekd25
27
0

Homework Statement


When the power factor of RLC circuit is equal to one, the frequency of the voltage source is 3 x 10^3 Hz. The rms value of the voltage source is 139 Volts and at a frequency of 3 x 10^3 Hz, the rms current in the circuit is 37.1 amps. If the inductive reactance at 3 x 10^3 Hz is 47 Ohms, what is the average power of the circuit in Watts at 0.78 times the resonant frequency of the circuit?

Homework Equations



Pav = Vrms Irms cos (|)
Vrms= V/sqrt 2
Irms= I/sqrt 2
V= XL I
V= Xc I
XL= 2 pi f L
Xc= 1/ 2 pi C
Res freq= 1/2pi 1/ sqrt (LC)

The Attempt at a Solution


I'm going in circles with this problem. Given the RMS value of the voltage and current, I tried to find the max voltage and current, and then plug that into V=XL I and V= Xc I to find XL and Xc, but I am probably wrong.

I guess I need to use the XL and Xc for each at the given frequency, to find both L and C to find the resonance frequency, multiply that number by .78, and then plug everything back into something?

Can someone please help me sort out this problem? Thanks
 
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  • #2
Can someone please help me out and get me started in the right direction please?
 
  • #3
If the power factor cos([tex]\varphi[/tex]) = 1, then the phase angle between the Vmax and Imax vectors in the phasor diagram must be [tex]\varphi[/tex] = 0. This means that Vmax vector has no y component, which means XL = XC. Since we know the inductive reactance and the resonant frequency, we can find the inductance and capacitance of the circuit. Also, at the resonant frequency, the impedance z = sqrt( R^2 + (XL -XC)^2 ) = sqrt( R^2 ) = R, so you can use Vrms and Irms to find R ( Vrms = Irms*z = Irms*R ). Then, you can find the reactances and impedance at the new frequency, draw the phasor/impedance diagram, find the new phase angle [tex]\varphi[/tex] between V and I ( [tex]\varphi[/tex] = tan^(-1)( (XL -XC) / R), and use those to calculate Pav.
 

1. What is an RLC circuit?

An RLC circuit is an electrical circuit that contains a resistor, inductor, and capacitor, connected in series or in parallel. These components are used to control the flow of current and voltage in the circuit.

2. How do you calculate the average power in an RLC circuit?

The average power in an RLC circuit can be calculated using the formula P = Vrms x Irms x cos(θ), where Vrms is the root mean square voltage, Irms is the root mean square current, and θ is the phase difference between them. Alternatively, it can be calculated using the formula P = I²R, where I is the rms current and R is the resistance of the circuit.

3. What factors affect the average power in an RLC circuit?

The average power in an RLC circuit is affected by the resistance, inductance, and capacitance values of the components, as well as the frequency of the AC power source. It is also affected by the phase difference between the voltage and current in the circuit.

4. How does the average power in an RLC circuit change over time?

The average power in an RLC circuit can change over time due to fluctuations in the voltage, current, and phase difference. It can also change over time as the components in the circuit heat up, causing changes in their resistance and inductance values.

5. How is the average power in an RLC circuit used in practical applications?

The average power in an RLC circuit is used to calculate the efficiency of the circuit and to determine the power losses in the components. It is also used to design and optimize circuits for specific applications, such as power distribution systems, electronic filters, and oscillators.

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