Domanda del libro di testo
A 0.30 μF capacitor is connected across an AC generator that produces a peak voltage of 10 V. What is the peak current to and from the capacitor if the emf frequency is 100 Hz?
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Ch 32: AC Circuits
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- 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: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 32, Problema 8a
The peak current to and from a capacitor is 10 mA. What is the peak current if the emf frequency is doubled?
Guida verificata passo dopo passo1
Understand the relationship between the current through a capacitor and the frequency of the applied emf. The current through a capacitor is given by the formula: where is the current, is the capacitance, is the angular frequency, and is the peak voltage.
Recall that the angular frequency is related to the frequency by the equation: . Doubling the frequency will also double the angular frequency .
Since the current is directly proportional to the angular frequency , doubling the frequency will result in the current also being doubled.
The initial peak current is given as 10 mA. Therefore, if the frequency is doubled, the new peak current will be twice the initial peak current.
Conclude that the new peak current can be calculated as . Perform this multiplication to find the final value if needed.
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Concetti chiave
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Capacitive Reactance
Capacitive reactance (Xc) is the opposition that a capacitor offers to alternating current (AC) due to its capacitance. It is inversely proportional to both the frequency of the AC signal and the capacitance value, described by the formula Xc = 1/(2πfC). As frequency increases, capacitive reactance decreases, allowing more current to flow through the capacitor.
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Percorso guidato
08:02
Capacitors & Capacitance (Intro)
Ohm's Law in AC Circuits
Ohm's Law, which states that voltage (V) equals current (I) times resistance (R), also applies to AC circuits but must consider impedance (Z) instead of resistance. In capacitive circuits, the relationship between current and voltage is affected by the frequency of the AC signal, leading to variations in current as frequency changes.
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Percorso guidato
03:12Resistors in AC Circuits
Frequency and Current Relationship
In AC circuits, the frequency of the electromotive force (emf) directly influences the current flowing through capacitive components. When the frequency is doubled, the capacitive reactance decreases, resulting in an increase in peak current. This relationship is crucial for understanding how changes in frequency affect the behavior of capacitors in circuits.
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Percorso guidato
05:08Circumference, Period, and Frequency in UCM
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