Question

Explain the term ‘sharpness of resonance in the AC circuit’.

Answer 1

Hint: The sharpness of resonance in an AC circuit is associated with the resonance of an RLC circuit that is connected to a varying or alternating voltage. The resonance of the circuit is associated with the maximum current flow in the circuit for a given frequency of the input varying voltage that will maximize the current flow in the circuit.

Formula Used: We will be using the following formula,
 $ f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{{LC}}} $ where $ f $ is the frequency, $ L $ is the inductance of the circuit and $ C $ is the capacitance of the circuit

Complete step by step answer
When a varying/alternating input voltage is applied to an RLC circuit, there will be maximum current in the circuit when the frequency of the input voltage is equal to the resonant frequency of the RLC circuit which can be calculated as
 $ f = \dfrac{1}{{2\pi }}\sqrt {\dfrac{1}{{LC}}} $ where $ L $ is the inductance of the circuit and $ C $ is the capacitance of the circuit.
The sharpness of the resonance is associated with the Q-factor of the RLC circuit. The sharpness characterizes how fast the energy decays in an RLC circuit that is connected to an alternating voltage.
For a perfect LCR circuit, if we apply an input frequency of voltage that is equal to the characteristic frequency of the circuit, theoretically the circuit will not stop resonating and the sharpness of the circuit will be infinite.
However, for a real circuit, there is a bandwidth of frequencies around the resonant frequency such that if we apply a voltage that varies with a frequency that falls in this bandwidth, the circuit will resonate and there will be maximum current flowing in the circuit.
The sharpness of resonance in the AC circuit can also be defined as the selectivity of the circuit to resonate in a bandwidth of frequencies.

Note
The less the sharpness of the circuit, the larger range of frequencies the circuit will resonate at, and the larger the sharpness of the circuit, the lower bandwidth of frequencies will resonate with the circuit. Less sharp circuits are more damped and have high energy losses while more sharp circuits are less damped and fewer energy losses.