Question

Define the quality factor of resonance in the series LCR circuit.

Answer 1

Hint: first understand the LCR circuit. The sharpness of an LCR circuit is measured by the quality factor in an LCR circuit. LCR circuit consists of capacitor, inductor, resistor connected in series or parallel. Using phasor, we can understand the LCR circuit better. Using the above statement, we can define the quality factor.

Complete step by step solution:
Sharpness of an LCR circuit can be measured using the quality factor. The sharpness of an LCR circuit is measured by the quality factor in an LCR circuit. It is a dimensionless quantity. The larger the sharpness of resonance sharper is the Q factor. Resonance occurs in a circuit that is connected in series when the supply frequency causes the voltage across the inductor and capacitor to be equal.

The $Q$ factor is the energy stored per unit cycle to the energy dissipated per cycle. Higher the $Q$ factor means more energy is stored. The quality factor controls the damping of oscillations. It is underdamped if the Q factor is less than half. Oscillation will be sustained longer.

Q factor will be affected if there is a resistive loss. $Q$ factor is a unitless dimensionless quantity. $Q$ factor can be defined as to how quickly the energy of the oscillating system decays. When the sharpness increases then damping increases and when damping decreases the sharpness decreases.
$Q={\displaystyle \frac{V_L}{V_R}}={\displaystyle \frac{\omega \times L}{R}}$
$Q$ is the quality factor,$R$ is the resistance, $L$ is the inductance.$V_L$ is the voltage across the inductor.

Note: Here in the solution we have used the potential across the inductor, but we can also use potential across the capacitor. $Q$ factor is the energy stored per unit cycle to the energy dissipated per cycle. Higher the Q factor means more energy is stored. The quality factor controls the damping of oscillations. It is a dimensionless quantity.