learning workings of inductor

steveb

Joined Jul 3, 2008
2,436
Once again, I offer my thanks, Steve.

Please have a look on the attachment. If there is any confusion, please let me know so that I can clarify it. You might also need to have a look on this diagram from my previous post. Please help me. Thanks.

With best regards
PG
Try this specific example and work it out exactly by both methods. Do you get the same answer, or different answers? In general, the average power is not equal to the average voltage times the average current. There may be special cases where it is true, but not in general. Do you feel this is a special case where it is true? If it is, you can try the functions and see if it works. But, why deal with this complication if you don't need to.
 

Thread Starter

PG1995

Joined Apr 15, 2011
832
Try this specific example and work it out exactly by both methods. Do you get the same answer, or different answers? In general, the average power is not equal to the average voltage times the average current. There may be special cases where it is true, but not in general. Do you feel this is a special case where it is true? If it is, you can try the functions and see if it works. But, why deal with this complication if you don't need to.
Thank you.

It seems special case to me. I didn't have any specific example with me. I was imagining how things work. I understand the purpose of your advice. I regard it. But don't you think by straightforwardly adopting the formulas kill the real spirit (if there is one!) of education. Shouldn't one be rather inquisitive, at least once in a while assuming your time and workload permit it?

Best wishes
PG
 
Last edited:

CraigHB

Joined Aug 12, 2011
127
The math provides the model that allows you to quantify what's going on. It's nice to be able to see things in your head without it, but there are lots of times where that approach breaks down. When putting several components together, there's no way you can obtain a quantatative understanding through conceptualization. That's why the math was developed in the first place.

For inductors, you need a conceptual understanding of magnetic flux and how it interacts with a conductor. If you want to start looking at waveforms after that, it's straight to the math or a simulation (which does the math for you).

You'd be better off understanding the math without understanding the concept than understanding the concept without understanding the math.
 

steveb

Joined Jul 3, 2008
2,436
It seems special case to me. I didn't have any specific example with me. I was imagining how things work.
Actually, you do have a specific example in post #16. You can calculate out the formulas for the waveforms and apply the calculations to it.

I understand the purpose of your advice. I regard it. But don't you think by straightforwardly adopting the formulas kill the real spirit (if there is one!) of education. Shouldn't one be rather inquisitive, at least once in a while assuming your time and workload permit it?
I'm not sure that you understood the purpose of my advice, due to my poor wording. To clarify, I agree with what you say here. What I'm suggesting (if your workload permits, or course) is to explore your inquisitiveness directly. Work out your method for the specific example and see if it works. Compare this to an example where voltage and current are constants. Then compare to voltage and currents that are ramps V(t)=k1*t and I(t)=k2*t. After all, my answer to your question could be wrong. I'm not infallible (at least, according to my wife :p), and if you were to show that your method gives the correct answer, I'd have to rethink my answer, or try to come up with a counter-example to show that you just happened to stumble on special cases.

My last comment about "why deal with that complication ..." was meant to refer to the whole approach of integrating power over time to find the stored energy. The formula E=0.5*L*I^2 gives the energy directly. By all means explore the alternative method for learning purposes, but it's not really the practical way to get the answer.
 

steveb

Joined Jul 3, 2008
2,436
Hi

Please have a look on the linked pages below. I'm sorry if some parts don't make much sense. Please help me. Thank you.

Page #1: http://img713.imageshack.us/img713/3874/imgdzs.jpg
Page #2: http://img685.imageshack.us/img685/8296/img0003rt.jpg
Link #1: http://img839.imageshack.us/img839/879/img0001uu.jpg

Thanks,
PG
For Q1, you have to be careful. The reactance shown for the capacitor is really the magnitude of reactance. Generally, reactance is a complex number, and for a capacitor or coil it is an imaginary number, while for a resistor, it is a real number. This is why the peak values, or the rms values are used to calculate the magnitude. The peak and rms values don't depend on time for a steady state sinusoidal signal, so it is appropriate to use them for the magnitude of reactance. The phase delay needs to be considered to get the phase angle.

For a capacitor, Xc=1/(jwC), where j is the square root of -1. This is a -90 degree phase shift in current, with the magnitude of reactance being 1/(wC).

For Q2, you also have to be very careful. The use of switches is not relevant when you are talking about sinusoids in steady state. Pure sinusoids are assumed to exist for all time into the past and all time into the future. So, when we talk about reactances, we are assuming that any switching transients have died away long ago. Your explanation is not quite correct, but your intuition is correct that the pure sinusoidal responses do not immediately start as soon as the switch is thrown. Instead there is an initial transient, which you can calculate, that needs time to decay to zero. After sufficient time, which depends on the system dynamics, the sinusoids will obey the reactance formula for the circuit in question.
 
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