# Q of a circuit

## What is Q

The Q or Quality factor of a resonant circuit is the ratio of stored power to dissipated power in the Reactance and Resistance of the circuit.

Generally speaking, a higher Q corresponds to a narrower bandwidth.

## How is Q calculated?

Note that at resonance, a series circuit "appears" to be purely resistive (it behaves like a resistor). Below resonance it appears to be capacitive (it behaves like a capacitor), and above resonance it appears to be inductive (behaves like an inductor)

$Q=\frac{P_{stored}}{P_{dissipated}}=\frac{I^2X}{I^2R}=\frac{X}{R}$ where:

• X = capacitive or inductive reactance at resonance
• R = series resistance
• P = Power
• I = Current

This formula is for all series resonant circuits and also works for parallel resonant circuits in which a small resistor is in series with the inductor.

If there is a large resistor in parallel with both the inductor and the capacitor, the formula becomes:

$Q=\frac{P_{dissipated}}{P_{stored}}=\frac{I^2R}{I^2X}=\frac{R}{X}$

For a given circuit element , the admittance is the reciprocal of the impedance.

Admittance is most useful in parallel AC circuit calculations where there are no series components. The equivalent admittance of a parallel circuit is the sum of the admittances of the components.

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