- Quality Factor Definition: The quality factor (Q factor) is defined as the ratio of reactance to resistance, indicating efficiency at a given frequency.
- Inductor Quality Factor: The Q factor of an inductor is the ratio of its reactance to its resistance, calculated as Q = ωL / R.
- Energy in Inductor: The energy stored in an inductor is based on the peak current through it, with power dissipation determined by its resistance.
- Quality Factor of Capacitor: The quality factor of a capacitor is the ratio of its reactance to its series resistance, given by Q = 1 / (ωRC).
- Lossy Capacitor: A lossy capacitor can be modeled with a capacitance and high parallel resistance, influencing its efficiency.
Quality Factor of Inductor
Every inductor has a small resistance along with its inductance. Lower resistance means a higher quality coil. The quality factor (Q factor) of an inductor at the operating frequency ω is defined as the ratio of the coil’s reactance to its resistance.
Thus for a inductor, quality factor is expressed as,
Where, L is the effective inductance of the coil in Henrys and R is the effective resistance of the coil in Ohms. As the unit of both resistance and reactance is Ohm, Q is a dimensionless ratio.
The Q factor may also be defined as
To prove this, consider a sinusoidal voltage V with frequency ω applied to an inductor L with internal resistance R, as shown in Figure 1(a). Let Im be the peak current through the inductor.
Then the maximum energy stored in the inductor
Figure 1. RL and RC circuits connected to a sinusoidal voltage sources
The average power dissipated in the inductor per cycle 
Hence, the energy dissipated in the inductor per cycle
Hence,
Quality Factor of a Capacitor
Figure 1(b). shows a capacitor C with small series resistance R associated within. The Q-factor or the quality factor of a capacitor at the operating frequency ω is defined as the ratio of the reactance of the capacitor to its series resistance.
Thus,
In this case also, the Q is a dimensionless quantity since the unit of both reactance and resistance is the same and it is Ohm. Equation (2) giving the alternative definition of Q also holds good in this case. Thus, for the circuit of Figure 1(b), on application of a sinusoidal voltage of value V volts and frequency ω, the maximum energy stored in the capacitor.
Where, Vm is the maximum value of voltage across the capacitance C.
But if
then
Where, Im is the maximum value of current through C and R.
Hence, the maximum energy stored in capacitor C is 
Energy dissipated per cycle
So, the quality factor of capacitor is
A lossy capacitor is often represented by a capacitance C with a high resistance Rp in parallel, as shown in Figure 2.
Then for the capacitor of Figure 2, the maximum energy stored in the capacitor 
Where, Vm is the maximum value of the applied voltage. The average power dissipated in resistance Rp.
Figure 2. Alternative method of representing a lossy capacitor
Energy dissipated per cycle 
Hence, 
