Textbook Question
FIGURE EX32.24 shows voltage and current graphs for an inductor. What is the value of the inductance L?
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Ch 32: AC Circuits
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 32, Problem 22b
The peak current through an inductor is 10 mA. What is the peak current if the emf peak voltage is doubled (at the original frequency)?
Verified step by step guidance1
Understand the relationship between the peak current and the peak voltage in an inductor. The peak current \( I_{peak} \) in an inductor is related to the peak voltage \( V_{peak} \) by the formula: \( I_{peak} = \frac{V_{peak}}{\omega L} \), where \( \omega \) is the angular frequency and \( L \) is the inductance.
Note that the angular frequency \( \omega \) is given by \( \omega = 2 \pi f \), where \( f \) is the frequency. Since the problem states that the frequency remains unchanged, \( \omega \) and \( L \) are constants in this scenario.
When the peak voltage \( V_{peak} \) is doubled, substitute \( 2V_{peak} \) into the formula for \( I_{peak} \): \( I_{peak} = \frac{2V_{peak}}{\omega L} \).
Compare the new peak current to the original peak current. The original peak current is \( I_{original} = \frac{V_{peak}}{\omega L} \). The new peak current is twice the original peak current because \( \frac{2V_{peak}}{\omega L} = 2 \cdot \frac{V_{peak}}{\omega L} \).
Conclude that doubling the peak voltage results in doubling the peak current. Therefore, the new peak current is \( 2 \cdot 10 \text{ mA} \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inductance
Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. The inductance value, measured in henries (H), determines how much voltage is induced across the inductor when the current changes. This relationship is crucial for understanding how inductors respond to changes in current and voltage.
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Ohm's Law
Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This fundamental principle, expressed as V = IR, is essential for analyzing circuits, including those with inductors, as it helps determine how changes in voltage affect current.
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03:07Resistance and Ohm's Law
Peak Voltage and Current Relationship
In AC circuits, the peak voltage and peak current are related through the impedance of the circuit, which includes resistance and reactance. When the peak voltage is increased while keeping the frequency constant, the peak current will also increase, assuming the impedance remains unchanged. This relationship is vital for predicting how changes in voltage affect current in inductive circuits.
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Related Practice
Textbook Question
What are VR and VC if the emf frequency in FIGURE EX32.19 is 25 kHz?
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Textbook Question
A high-pass RC filter is connected to an AC source with a peak voltage of 10.0 V. The peak capacitor voltage is 6.0 V. What is the peak resistor voltage?
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Textbook Question
An inductor is connected to a 15 kHz oscillator. The peak current is 65 mA when the rms voltage is 6.0 V. What is the value of the inductance L?
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Textbook Question
What are VR and VC if the emf frequency in FIGURE EX32.19 is 2.5 kHz?
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Textbook Question
FIGURE EX32.24 shows voltage and current graphs for an inductor. What is the emf frequency f?
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