AC Advice

  1. Get to know ELI the ICE man. L and C are inductor and capacitor, E and I are voltage and current. ELI illustrates that in an inductor, E comes before I. If E is at its peak now, I will reach its peak a quarter of a cycle later. ICE shows that it is the other way around for the capacitor.
  2. If you are into calculus, explain the above phase differences mathematically. If you are at the algebra and trig level in math, sketch sine and cosine curves on the same graph. Let's say the sine is the I. Note that its maximum rate of change is when I = 0, and remember that inductor voltage is proportional to the rate of change of current. Thus the 90o phase difference between I and voltage for the inductor. For the capacitor, the maximum current occurs when the voltage is zero, and we get a 90o phase difference for C, also.

    Incidentally, this voltage being ahead of the current in the inductor and the opposite in the capacitor is really a convention. We could say it the other way around if we wanted to: if at some instant, side A of the capacitor is 5 volts above side B, we could say VC is +5 or -5, depending on how you choose to look at it. Here is the standard way of looking at it: Make the VR be in phase with I. For example, if you define left to right through a resistor to be the positive direction for I, then the left side is the side for positive V. Then if you continue going to the right (and eventually completing the circuit), the side of the L or C you come to first is the V with respect to the other side.

    Following this convention, if I is a sine, VR is a sine, VL is a cosine, and VC is a minus cosine.
  3. Play with those phasor diagrams. A lot.
  4. And a lot more.

For the series RLC circuit, the total opposition to current, the impedance Z, is given by Z = [R2 + (XL - XC)2]1/2 , where XL and XC are called the inductive and capacitive reactance. It can be shown that XL = w L and XC = 1/(w C), and these quantities express the opposition (in Ohms) to current in those individual elements. The angular frequency w in radian/second is 2p times the frequency in Hz. R, XL , XC and Z can be regarded as vectors as shown in the diagram below:

(The dotted line is XL - XC.)

The right triangle above is a consequence of the 90o phase angles discussed in #2 above. You can find these things derived in lots of texts on physics or on electrical circuits.

For R, C and L in parallel, the currents are out of phase, and you can use phasor currents V/R, V/XL and V/XC in the directions shown in the diagram above. The add the phasors (vector sum) to get the total current. Then while you are at it, find Z for the three in parallel by Z = V/I and you will find that Z = [R-2+(XL-1+XC-1)2]-1/2. This Z formula is not needed for the parallel only case because you can find the current without it. But for a combination series and parallel, it is useful.

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