Resonance in a series RLC Circuit
Resonance is a special condition in an RLC circuit that occurs when XL = XC. This happens at an angular frequency wo given by:
| woL |
= |
| 1
|  |
| woC
|
|
so |
wo2 |
= |
| 1
| |
| LC
|
|
This is the value we found for the natural oscillation frequency of the LC circuit, so we're driving it at its natural oscillation frequency. Some of the things that happen at resonance include:
- Z = R, which is the minimum possible value of Z
- the current in the circuit is maximized
- the phase angle is zero
- the power factor is 1
- all the power in the circuit is dissipated in the circuit (maximum power transfer)
Resonant RLC circuits are extremely useful. They're used in tuning radios as well as in metal detectors such as the ones you walk through at security checkpoints in airports.