Find the peak current and resonant frequency of the following circuit (as shown in figure).
$0.2 \mathrm{~A}$ and $50 \mathrm{~Hz}$
$0.2 \mathrm{~A}$ and $100 \mathrm{~Hz}$
$2 \mathrm{~A}$ and $100 \mathrm{~Hz}$
$2 \mathrm{~A}$ and $50 \mathrm{~Hz}$
Correct Option: 1
as given $\mathrm{z}=\sqrt{\left(\mathrm{x}_{\mathrm{L}}-\mathrm{x}_{\mathrm{C}}\right)^{2}+\mathrm{R}^{2}}$
$\mathrm{x}_{\mathrm{L}}=\omega_{\mathrm{L}}=100 \times 100 \times 10^{-3}=10 \Omega$
$\mathrm{x}_{\mathrm{C}}=\frac{1}{\omega_{\mathrm{C}}}=\frac{1}{100 \times 100 \times 10^{-6}}=10 \Omega$
$\mathrm{z}=\sqrt{(10-100)^{2}+\mathrm{R}^{2}}=\sqrt{90^{2}+120^{2}}$
$=30 \times 5=150 \Omega$
$\mathrm{i}_{\text {peak }}=\frac{\Delta \mathrm{v}}{\mathrm{z}}=\frac{30}{150}=\frac{1}{5} \mathrm{amp}=0.2 \mathrm{amp}$
\& For resonant frequency
$\Rightarrow \omega \mathrm{L}=\frac{1}{\omega \mathrm{C}} \Rightarrow \omega^{2}=\frac{1}{\mathrm{LC}} \Rightarrow \omega=\frac{1}{\sqrt{\mathrm{LC}}}$
$\& \mathrm{f}=\frac{1}{2 \pi \sqrt{\mathrm{LC}}} \Rightarrow \frac{1}{2 \pi \sqrt{100 \times 10^{-3} \times 100 \times 10^{-6}}}$
$=\frac{100 \sqrt{10}}{2 \pi}=\frac{100 \pi}{2 \pi}=50 \mathrm{~Hz}$
as $\sqrt{10} \approx \pi$
Answer (1)
- JEE Main
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- Physics
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- Friction
- Work, Power, Energy
- Centre of Mass and Collision
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- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
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- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
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- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
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- 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,
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,