Answer
Verified
64.8k+ views
Hint: In order to solve this question one should be aware of the concept of resonance and the conditions of resonance in an LCR circuit. The condition of the resonance depends on a particular frequency, also known as resonance frequency. When the frequency of the LCR is equal to the resonance frequency only then the condition of resonance is attained.
Complete step by step solution:
The condition for resonance in the LCR circuit is given by,
${\omega _o} = \dfrac{1}{{\sqrt {LC} }}$
Here, we can easily observe that the amplitude of the current is maximum at the resonance frequency ${\omega _o}$ . Since, ${i_m} = {V_m}IR$ at resonance, the amplitude of current for case ${R_2}$ is sharper to that for case ${R_1}$ . The quality factor or can be said as the Q-factor of a resonance LCR circuit is defined as the ratio of voltage drop across the capacitor to that of applied voltage.
It is given by,
$Q = \dfrac{1}{R}\sqrt {\dfrac{L}{C}} $
The Q-factor or Quality factor determines the sharpness of the resonance curve. If the resonance curve is less sharp, then the maximum current decreases and also the circuit is close to the resonance for a larger range $\Delta \omega $ of frequencies and the regulation of the circuit then will not be good. Therefore, the sharp resonance curve is better.
Note: Less sharp the resonance is better, as for less sharp resonance curve, less is the selectivity of the circuit while the Q-Factor will be higher, sharper is the resonance curve and lesser will be the loss in energy of the circuit.
Complete step by step solution:
The condition for resonance in the LCR circuit is given by,
${\omega _o} = \dfrac{1}{{\sqrt {LC} }}$
Here, we can easily observe that the amplitude of the current is maximum at the resonance frequency ${\omega _o}$ . Since, ${i_m} = {V_m}IR$ at resonance, the amplitude of current for case ${R_2}$ is sharper to that for case ${R_1}$ . The quality factor or can be said as the Q-factor of a resonance LCR circuit is defined as the ratio of voltage drop across the capacitor to that of applied voltage.
It is given by,
$Q = \dfrac{1}{R}\sqrt {\dfrac{L}{C}} $
The Q-factor or Quality factor determines the sharpness of the resonance curve. If the resonance curve is less sharp, then the maximum current decreases and also the circuit is close to the resonance for a larger range $\Delta \omega $ of frequencies and the regulation of the circuit then will not be good. Therefore, the sharp resonance curve is better.
Note: Less sharp the resonance is better, as for less sharp resonance curve, less is the selectivity of the circuit while the Q-Factor will be higher, sharper is the resonance curve and lesser will be the loss in energy of the circuit.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
Other Pages
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
According to classical free electron theory A There class 11 physics JEE_Main
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main