AC Electrics -Introduction to AC — Page 174, Lesson 181

I want to walk you through the concept of impedance in AC circuits. This is the total opposition to current flow in an AC circuit, and it’s a combination of three things: resistance, inductive reactance, and capacitive reactance. But here’s the key problem — you can’t just add them together like simple numbers. Why? Because in each type of component, the voltage and current have a different phase relationship — they don’t peak at the same time. So the opposition they offer isn’t aligned in time, and that means simple addition doesn’t work. Let me define those two types of reactance more clearly. Inductive reactance — that’s the opposition to current change caused by an inductor — has the opposite effect to capacitive reactance, which is the opposition caused by a capacitor. In an inductive circuit, the current lags the voltage by 90 degrees. In a capacitive circuit, the current leads the voltage by 90 degrees. So these two reactances are 180 degrees apart in phase — they directly oppose each other. That means the total reactance in a circuit can be found by simply subtracting one from the other. If you have both an inductor and a capacitor, the net reactance is the difference between the inductive and capacitive reactance. Now, impedance — given the symbol Z and measured in ohms — is the vector sum of the resistance and that total reactance. A vector sum means you have to account for the fact that resistance and reactance are 90 degrees out of phase with each other. We can picture this using an impedance triangle, which is shown in Figure 11.13. In that triangle, resistance is drawn horizontally, and reactance is drawn vertically — at a right angle — because they are 90 degrees apart. The hypotenuse of that triangle is the impedance. Mathematically, we use Pythagoras’ Theorem to calculate it: Z squared equals R squared plus X total squared, where X total is the net reactance. Let’s move on to resonant circuits. This is a really important idea. When you change the supply frequency in a circuit, it affects inductance and capacitance in opposite ways. If you increase the supply frequency, the inductive reactance (XL) increases — that’s because the inductor opposes faster changes more strongly. At the same time, the capacitive reactance (XC) decreases — a capacitor actually passes more current at higher frequencies. So increasing XL tends to decrease the current, while decreasing XC tends to increase the current. They pull in opposite directions. Because they react oppositely to frequency changes, there will be one specific frequency for each circuit where the inductive reactance and capacitive reactance become equal. When that happens — when XL equals XC — the circuit is said to be resonant. That’s the definition: a resonant circuit is one where capacitive reactance and inductive reactance are equal. Now, what happens at resonance depends on how the components are connected. If the capacitor and inductor are placed in series with each other, at the resonant frequency the current flowing in the circuit will be maximum. If, on the other hand, they are placed in parallel with each other, at the resonant frequency the current will be at a minimum. So series resonance gives you maximum current; parallel resonance gives you minimum current. Let me give you a quick summary mnemonic that helps remember the phase relationships. It goes: C I V I L. In a Capacitive circuit, I current leads V voltage leads I current in an L inductive circuit. So for a capacitor: current leads voltage. For an inductor: current lags voltage. That’s captured in the mnemonic. Finally, let’s talk about power in AC circuits. In a DC circuit, according to Ohm’s Law, power is simply voltage times current. The same formula applies in AC circuits — but there’s a catch. Because of the phase shift between voltage and current in reactive circuits, the actual power absorbed is not necessarily the same as the power apparently supplied. The apparent power is the product of the RMS voltage and RMS current, but the real power — the power actually dissipated as heat or work — depends on the phase angle between them. We’ll look at resistive, inductive, and capacitive circuits separately, and then a practical circuit that has a combination of all three.