Average power used by circuit?

In summary, the problem involves calculating the average power P(at 402 Hz) being used by a circuit with an rms voltage of 149 V, a resistance of 298 Ω, a capacitance of 4.1 μF, and an inductance of 0.23 H. Using the equations V=IR, Avg power=Vrms*Irms(cos phase angle), vrms=vmax/(sqrt 2), and Irms=Imax/(sqrt 2), the solution involves finding the rms current, which is 0.35355, and the phase angle, which is 58.4 degrees. The average power can then be calculated by multiplying the rms current by the voltage and the cosine of the
  • #1
icyspicy
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Homework Statement



If the rms voltage across the generator is 149 V, calculate the average power P(at 402 Hz) being used by the circuit.

R = 298 Ω, a capacitance C = 4.1 μF, inductance of L = 0.23 H

https://tycho-s.physics.wisc.edu/cgi/courses/shell/common/showme.pl?courses/phys104/spring09/homework/07/rclseries/ex2s92p4.gif [Broken]


Homework Equations



V=IR
Avg power=Vrms*Irms(cos phase angle)
vrms=vmax/(sqrt 2)
Irms=Imax/(sqrt 2)

The Attempt at a Solution



Vrms=IrmsR
149/(sqrt 2)=Irms*298 I think that the 149 V given in the problem needs to be divided by 2 to get Vrms? is rms voltage across generator same as max voltage? I'm not exactly sure about that part...anyways I got:
Irms=.35355
Avg power= (.35355)(149/sqrt 2) cos (phase angle)
i solved for XL (581) and XC (96.6), which were both correct. so I got the phase angle to be 58.4 degrees
Avg power= (.35355)(149/sqrt 2) cos (58.4)

I'm not getting the right answer, so maybe my approach was wrong? Any help is appreciated.
 
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  • #2
nevermind, got it
 
  • #3



Your approach is correct, but there may be a calculation error in your attempt at a solution. The rms voltage is indeed equal to the maximum voltage divided by the square root of 2. The phase angle can be calculated using the formula tanθ = XL-XC/R (where XL and XC are the reactances of the inductor and capacitor, respectively). Once you have the phase angle, you can use the formula for average power to calculate the final answer. Double check your calculations and make sure you are using the correct values for the reactances and resistance.
 

1. What is the formula for calculating average power used by a circuit?

The formula for average power used by a circuit is P = VI, where P represents power in watts, V represents voltage in volts, and I represents current in amperes.

2. How is average power different from instantaneous power?

Average power is the average rate at which energy is transferred or used by a circuit over a period of time, while instantaneous power refers to the power used at a specific moment in time.

3. Can average power be negative?

Yes, average power can be negative if the circuit is consuming more power than it is generating. This can happen in circuits with resistive elements like resistors or inductive elements like inductors.

4. How does changing the voltage or current affect the average power used by a circuit?

Changing the voltage or current will directly affect the average power used by a circuit. Increasing either the voltage or current will result in an increase in average power, while decreasing either will result in a decrease in average power.

5. Is average power the same as energy?

No, average power and energy are not the same. Average power is a measure of the rate at which energy is used, while energy is a measure of the total amount of work done or heat transferred. Average power is measured in watts, while energy is measured in joules.

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