Question:
In a series LCR circuit, the inductive reactance $\left(\mathrm{X}_{\mathrm{L}}\right)$ is $10 \Omega$ and the capacitive reactance $\left(\mathrm{X}_{\mathrm{C}}\right)$ is $4 \Omega$. The resistance (R) in the circuit is $6 \Omega$. The power factor of the circuit is :
$\frac{1}{2}$
$\frac{1}{2 \sqrt{2}}$
$\frac{1}{\sqrt{2}}$
$\frac{\sqrt{3}}{2}$
Correct Option: , 3
Solution:
We know that power factor is $\cos \phi$,
$\cos \phi=\frac{R}{Z}$ ..........(1)
$Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}}$ .......(2)
$(\omega \mathrm{L}-1 / \omega \mathrm{C})$
$\Rightarrow Z=\sqrt{6^{2}+(10-4)^{2}}$
$\Rightarrow Z=6 \sqrt{2} \mid \cos \phi=\frac{6}{6 \sqrt{2}}$
$\cos \phi=\frac{1}{\sqrt{2}}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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