Resonance in a Circuit

At resonance, the circuit appears resistive. This means that the impedance of the circuit is purely resistive, with no reactance. This occurs when the inductive reactance (XL) of an inductor and the capacitive reactance (XC) of a capacitor cancel each other out.

Inductive Reactance
- An inductor is a passive electronic component that opposes changes in current flow. It stores energy in a magnetic field.
- Inductive reactance (XL) is the opposition to the change in current caused by an inductor. It is directly proportional to the frequency of the applied alternating current (AC).
- Inductive reactance can be calculated using the formula XL = 2πfL, where f is the frequency and L is the inductance of the inductor.

Capacitive Reactance
- A capacitor is a passive electronic component that stores energy in an electric field. It opposes changes in voltage.
- Capacitive reactance (XC) is the opposition to the change in voltage caused by a capacitor. It is inversely proportional to the frequency of the applied AC.
- Capacitive reactance can be calculated using the formula XC = 1 / (2πfC), where f is the frequency and C is the capacitance of the capacitor.

Impedance and Resonance
- Impedance (Z) is the total opposition to the flow of alternating current in a circuit. It is the combination of resistance (R) and reactance (X).
- At resonance, the inductive reactance and capacitive reactance cancel each other out, resulting in a purely resistive impedance.
- The formula for calculating impedance is Z = R + j(XL - XC), where j is the imaginary unit.
- When XL = XC, the imaginary terms cancel out, leaving only the resistive term (R).

Conclusion
At resonance, the circuit appears resistive because the inductive reactance and capacitive reactance cancel each other out, resulting in a purely resistive impedance. This occurs when the frequency of the applied AC is such that XL = XC.