Domanda del libro di testo
A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V. What is the capacitance?
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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
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Capitolo 32, Problema 12b
A capacitor has a peak current of 330 μA when the peak voltage at 250 kHz is 2.2 V. If the peak voltage is held constant, what is the peak current at 500 kHz?
Guida verificata passo dopo passo1
Understand the relationship between the current and frequency in a capacitor. The current through a capacitor is given by the formula: , where is the current, is the voltage, is the angular frequency, and is the capacitance.
Recall that angular frequency is related to the frequency by the formula: . Therefore, the current is proportional to the frequency when the voltage and capacitance are constant.
Set up the proportionality relationship between the peak currents and frequencies: , where and are the peak currents at frequencies and , respectively.
Substitute the given values into the proportionality equation: . Solve for by multiplying both sides by 330 μA.
Conclude that the peak current at 500 kHz is twice the peak current at 250 kHz, as the frequency has doubled. This means .
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Concetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Capacitance
Capacitance is the ability of a capacitor to store electrical charge per unit voltage. It is measured in farads (F) and is defined by the formula C = Q/V, where C is capacitance, Q is charge, and V is voltage. The capacitance value influences how much current can flow through the capacitor at a given frequency.
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Percorso guidato
08:02
Capacitors & Capacitance (Intro)
Impedance in AC Circuits
In alternating current (AC) circuits, capacitors exhibit impedance, which is the opposition to current flow. The impedance of a capacitor decreases with increasing frequency, calculated as Z = 1/(2πfC), where Z is impedance, f is frequency, and C is capacitance. This relationship is crucial for understanding how current changes with frequency.
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Percorso guidato
08:40Impedance in AC Circuits
Current-Frequency Relationship
The peak current through a capacitor in an AC circuit is directly proportional to the frequency of the applied voltage and the capacitance. As frequency increases, the peak current also increases, assuming constant voltage. This relationship can be expressed as I = C * dV/dt, where I is current, C is capacitance, and dV/dt is the rate of change of voltage.
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Percorso guidato
05:08Circumference, Period, and Frequency in UCM
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