Question

What is the Q factor formula for series RL circuit?

Answer 1

The **Q factor** (Quality factor) for a series **RL circuit** is a measure of the sharpness of the resonance peak in the frequency response. It gives an indication of how underdamped an oscillator or resonator is, and is defined as the ratio of the inductive reactance to the resistance in the circuit.

The formula for the **Q factor** of a series RL circuit is:

\[
Q = \frac{\omega L}{R}
\]

Where:
- \( Q \) = Quality factor (dimensionless)
- \( \omega \) = Angular frequency of operation = \( 2\pi f \) (in radians per second)
- \( L \) = Inductance (in henries, H)
- \( R \) = Resistance (in ohms, Ω)
- \( f \) = Frequency of operation (in hertz, Hz)

### Explanation:
- **Inductive Reactance**: In a series RL circuit, the inductive reactance is \( X_L = \omega L \). This opposes the current and depends on the frequency of the signal.
- **Resistance (R)**: This represents the real part of the impedance in the RL circuit and causes energy dissipation in the form of heat.

The Q factor is higher for circuits with lower resistance and higher inductance, indicating a more selective or sharp resonance characteristic.

Answer 2

The Q factor (or quality factor) of a series RL (resistor-inductor) circuit is a measure of the circuit's selectivity or sharpness of resonance. For a series RL circuit, the Q factor is defined as the ratio of the inductive reactance (\(X_L\)) to the resistance (\(R\)).

Here’s the formula for the Q factor in a series RL circuit:

\[ Q = \frac{X_L}{R} \]

where:
- \(X_L\) is the inductive reactance, given by \(X_L = 2 \pi f L\), where \(f\) is the frequency of the signal and \(L\) is the inductance of the coil.
- \(R\) is the resistance of the resistor in the circuit.

In summary:

\[ Q = \frac{2 \pi f L}{R} \]

This formula shows that the Q factor increases with higher inductance and frequency, and decreases with higher resistance.