Textbook Question
What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz?
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Ch 31: Alternating Current
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 31, Problem 4a
A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?
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Understand the relationship between voltage and current in an AC circuit with a capacitor. In such a circuit, the current leads the voltage by a phase angle due to the capacitive reactance.
Recall the formula for the phase angle \( \Phi \) in a capacitive circuit, which is given by \( \Phi = -\frac{\pi}{2} \). This indicates that the voltage lags the current by 90 degrees.
Recognize that the negative sign in the phase angle formula indicates that the voltage lags behind the current.
Since the phase angle \( \Phi \) is \( -\frac{\pi}{2} \), the source voltage lags the current by 90 degrees.
Conclude that in a purely capacitive AC circuit, the phase angle is always \( -\frac{\pi}{2} \), meaning the voltage lags the current by 90 degrees.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Capacitive Reactance
Capacitive reactance (Xc) is the opposition a capacitor offers to the flow of alternating current (AC). It is inversely proportional to the frequency (f) of the AC source and the capacitance (C) of the capacitor, given by the formula Xc = 1/(2πfC). This concept is crucial for understanding how the capacitor affects the phase relationship between voltage and current.
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Capacitors & Capacitance (Intro)
Phase Angle in AC Circuits
The phase angle (Φ) in AC circuits indicates the difference in phase between the voltage across and the current through a component. For a purely capacitive circuit, the current leads the voltage by 90 degrees, meaning the phase angle is -90 degrees. This concept helps determine whether the voltage leads or lags the current in the circuit.
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Voltage and Current Relationship in Capacitors
In capacitors connected to an AC source, the current leads the voltage because the capacitor charges and discharges, causing the current to reach its peak before the voltage does. This relationship is essential for understanding the behavior of capacitors in AC circuits and determining the phase angle between voltage and current.
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Related Practice
Textbook Question
You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?
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Textbook Question
A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the capacitance C of the capacitor if the current amplitude is 5.30 A?
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Textbook Question
The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1) v = Vcosωt. The voltage amplitude is V = 45.0 V. What are (a) the root-mean-square potential difference Vrms and (b) the average potential difference Vav between the two terminals of the power supply?
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Textbook Question
What is the inductance of an inductor whose reactance is 120 Ω at 80.0 Hz?