Solve RLC circuit for wattage

[Mayobe]

Hello.

 

I'm taking a pre-calc course and I came across a bizzare question that I have no idea about. I really have very little interest in electrical engineering (sorry), but I'm trying to figure out how to turn this question into mathematics so I can solve it.

 

First we're given the equation P = VI cos θ. P is in watts, V is effective voltage, I is effective current and theta is the phase angle between current and voltage. We're given V, then told that the circuit has a resistor with set ohms, an inductor with set mH and a capacitor with set μF. The frequency is also provided in Hz. We're asked to determine the value of P in mW.

 

I've been browsing the web for quite a while now and I can't make head nor tail of the things I've seen. I just want to turn this into math so I can do something with it apart from writing 'I am not an electrical engineer.' as the answer.

 

I'm fine with calc and vectors don't scare me, I just don't understand what all these different terms mean (like phi vs theta for angles and X or Z or etc.) and I don't grasp the process used to get the V, I and theta that I need.

 

Any advice would be greatly appreciated.

Edited February 27, 2013 by Mayobe

[Izzy_Bee]

Respectively P = VI cos θ. is the maths calculation, you just need to input the correct values in the correct place.

 

With asking you to find the power, they're simply asking you to find energy change, over time taken.

Try working out what V is with the ohms, mH, uF and Hz taken away, that will give you V.

Because the inductor is dependant on the frequency, and you haven't given either, I've put numbers where I can in the initial places and used capacitance and inductor equations to reverse my way around your question, but that is digging deeper into an area you're unsure of: engeering.

 

So when looking at this, with my own examples: I try to balance it up, as you've not supplied ANY numbers at all that you said you were given, and 2 or 3 would have really helped a lot, with me giving an example.

What I've been trying to do is subject my own numbers, but because there is a frequency and an inductor as well as capacitor those numbers don't have to be just ANY number they have to be very specific to the 6th decimal place, again hard as I don't start with anything.

 

Could you supply your questions with the actual powers you were given?

 

Just some additional info haha:

A capacitor doesn't increase power as such, it builds a charge in a circuit (say circuit 1v) the capacitor works between to conductive plates and insulator I.e air, the charge builds on one plate (say again to 4v) and then discharges onto the other plate. This is useful in things like cameras with small batteries, the capacitor takes a charge and builds and discharges when you take a picture for the flash.

 

This is what I am currently at, without your specific values

 

The power P (in W) supplied to a series combination of elements in an ac circuit is P = VI cos theta , where V is the effective voltage, I is the effective current, and theta is the phase angle between the current and voltage .

If V = 225 mV across an RLC circuit with a resistor ( R = 42.0 ohms ), an inductor ( L = 42.9 mH), a capacitor ( C = 86.5 micro farad ), and a frequency of 61.0 HZ, determine the power supplied to these elements . P = ........... mW

 

Ahh that's as far as I can get with this and I hope it some how will help you.

[Mayobe]

Oh my gosh I found it. Thank you very much for your advice. It turns out my problem was with unit conversions.

 

The steps I took to get the correct answer were:

 

XL = 2pi*fL*10^-3 (for unit correction from mH to H)

XC = 1 / (2pi*fC*10^-6) (unit correction from micro F)

X = |XL - XC|

theta = atan(X/R)

Z = sqrt(R^2 + X^2)

I = V*10^-3/Z (correction from mV to V)

P = ((V*10^-3) * I * cos(theta)) watts

 

When I corrected that to mW it was correct. FINALLY!

 

Thank you for your help! I just needed one more nudge to get it to click for me.

[Izzy_Bee]

I'm glad I could have assited you in any way I managed too haha.

 

You might like to look in to some of the equations used in science, they're alays good to know and can be fun challenges at times too.

 

Have a good day!