
An AC circuit has\[R{\text{ }} = {\text{ }}100\Omega \], \[C{\text{ }} = {\text{ }}2\mu F\]and\[L{\text{ }} = {\text{ }}80{\text{ }}mH\]connected in series. The quality factor of the circuit is
1. \[20\]
2. $2$
3. $0.5$
4. $400$
Answer
163.5k+ views
Hint: Q factor or also called as quality factor of a circuit is nothing but a picture of efficiency of the circuit. It is ratio of total energy stored per cycle to energy dissipated per cycle. For an inductor, it can be explained as the ratio of its inductive reactance ${X_C}$ to resistance i.e. $Q = \frac{{{X_C}}}{R}$. If all energy is in the stored form and no energy is dissipated then it is the ideal case and such a circuit is an ideal circuit. Quality factor is a dimensionless quantity.
Complete answer:
Given that resistance, capacitance and inductance connected in series and values of each are as follows
Capacitance, \[C{\text{ }} = {\text{ }}2\mu F = 2{(10)^{ - 6}}F\]
Inductance, \[L{\text{ }} = {\text{ }}80{\text{ }}mH = 80{(10)^{ - 3}}H\]
Step 1: In resonance condition, capacitance reactance= inductance reactance.
${X_L} = {X_C}$
Step 2: Divide both sides by Resistance R
\[\frac{{{X_L}}}{R} = \frac{{{X_C}}}{R}\]
\[\omega L = \frac{1}{{\omega C}}\]
\[{\omega ^2} = \frac{1}{{LC}}\]
\[{\omega ^2} = \frac{1}{{80{{(10)}^{ - 3}}2{{(10)}^{ - 6}}}}\]
\[{\omega ^2} = 6.25{(10)^6}\]
Step 3: Taking square root
\[\omega = 2500\]
Step 4: Quality factor can be calculated by the formula
$Q = \frac{{\omega L}}{R}$
$Q = \frac{{2500(80){{(10)}^{ - 3}}}}{{100}}$
$Q = 2$
Hence the correct option is (2) and the correct value of quality factor Q is 2.
Note: Capacitance can be simply defined as storing of energy in the form of electric field whereas inductance is storing of energy in form of magnetic field. Quality factor is defined for resonance. Unit of inductance is henry(H) and unit of capacitance is farad(F). While performing calculation, micro farad and milli henry must be converted to farad and henry.
Significance of quality factor can be compared to that of a Carnot engine in thermodynamics. It is used to describe damping in a circuit.
Complete answer:
Given that resistance, capacitance and inductance connected in series and values of each are as follows
Capacitance, \[C{\text{ }} = {\text{ }}2\mu F = 2{(10)^{ - 6}}F\]
Inductance, \[L{\text{ }} = {\text{ }}80{\text{ }}mH = 80{(10)^{ - 3}}H\]
Step 1: In resonance condition, capacitance reactance= inductance reactance.
${X_L} = {X_C}$
Step 2: Divide both sides by Resistance R
\[\frac{{{X_L}}}{R} = \frac{{{X_C}}}{R}\]
\[\omega L = \frac{1}{{\omega C}}\]
\[{\omega ^2} = \frac{1}{{LC}}\]
\[{\omega ^2} = \frac{1}{{80{{(10)}^{ - 3}}2{{(10)}^{ - 6}}}}\]
\[{\omega ^2} = 6.25{(10)^6}\]
Step 3: Taking square root
\[\omega = 2500\]
Step 4: Quality factor can be calculated by the formula
$Q = \frac{{\omega L}}{R}$
$Q = \frac{{2500(80){{(10)}^{ - 3}}}}{{100}}$
$Q = 2$
Hence the correct option is (2) and the correct value of quality factor Q is 2.
Note: Capacitance can be simply defined as storing of energy in the form of electric field whereas inductance is storing of energy in form of magnetic field. Quality factor is defined for resonance. Unit of inductance is henry(H) and unit of capacitance is farad(F). While performing calculation, micro farad and milli henry must be converted to farad and henry.
Significance of quality factor can be compared to that of a Carnot engine in thermodynamics. It is used to describe damping in a circuit.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Degree of Dissociation and Its Formula With Solved Example for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Charging and Discharging of Capacitor

Wheatstone Bridge for JEE Main Physics 2025

Instantaneous Velocity - Formula based Examples for JEE

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main
