Calculating RLC Circuit Power with Frequency: Solutions & Equations

[Slepton]

Homework Statement

How do one calculate the power in time of RLC circuit in parallel combination running an AC current ? It has to be in terms of frequency (\omega = 2 \pi f )

Homework Equations

\omega = 1/ \sqrt{LC}

The Attempt at a Solution

I started off with the omega but could not reach all the way to an expression for power in terms of omega.

Thanks in advance

 

[berkeman]

Homework Statement

How do one calculate the power in time of RLC circuit in parallel combination running an AC current ? It has to be in terms of frequency (\omega = 2 \pi f )

Homework Equations

\omega = 1/ \sqrt{LC}

The Attempt at a Solution

I started off with the omega but could not reach all the way to an expression for power in terms of omega.

Thanks in advance

Welcome to the PF. You need to define the problem a bit more. An RLC circuit does not dissipate power unless driven by some source, and that source will have some source impedance. Otherwise, do you mean that the capacitor is charged up to some voltage at time t=0, and then the charging source is removed, and you want to plot the power dissipated versus time?

 

[Slepton]

sorry, I was vague. So, omega is the frequency of the power supply. I and V are the total current and voltages of the circuit. L, R, C are the inductance, resistance and capacitance. I have to find power consumption due to the parallel LCR circuit for a time 't'. I am told to express the power in I, V, R, omega, L or C in time 't'. If I and V are the total current and voltage, wouldn't power just be IV. But since it's AC circuit, I and V fluctuate.

 

[berkeman]

sorry, I was vague. So, omega is the frequency of the power supply. I and V are the total current and voltages of the circuit. L, R, C are the inductance, resistance and capacitance. I have to find power consumption due to the parallel LCR circuit for a time 't'. I am told to express the power in I, V, R, omega, L or C in time 't'. If I and V are the total current and voltage, wouldn't power just be IV. But since it's AC circuit, I and V fluctuate.

Still not enough information. Please post the exact text of the question, along with any diagrams. And post your work towards a solution. As you have read at the PF Rules link at the top of this page, we cannot help until you post your work.

 

[Slepton]

The question was made by my professor. So, that's all the info. it gives us. It reads exactly like this:

If you are using a parallel RLC circuit with omega as the frequency of the power supply, I and V as the total current and voltage of the circuit, write down an expression for the power consumption in terms of I, V, omega, R, L or C in 't' period of time.

What I did so far is wrote down power as P= V^2/Z = V_0 exp (2*(j*omega*t -j*phi))*(1/R + j(1/X_c - 1/X_L)). I got confused from here since, I am asked for power in time 't' and power already is work per unit time. so, does it mean that i have to again take derivative of P with respect to time?

 

[rl.bhat]

't' period of time.
What is the relation between 't' period of time and ω?

 

[Slepton]

If t was time period then t = 2*pi/omega, but from the question it sounds like t could be any time.

 

[Delphi51]

I'm the retired high school teacher hoping to learn something here, too.
Slepton, we teachers are not always perfect and your teacher has a mistake in the question - it is not correct to say "the power in time t". Rather you must say the "energy in time t" or the "power at time t". No doubt it is the latter we are looking for.

Now, I don't see how or why you got that complicated expression. To my high school mind, it should be just
P = V^2/Z = Vo^2*e^(2jwt) all divided by R + j(Xc - XL).

 

[rl.bhat]

In parallel RLC circuit, RL are in series and C is in parallel to it. In this circuit the power dissipation is in the resistance only. Hence P = [ V/( R + jωL )]^2*R where V = Vosin(ωt)