Textbook Question
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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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 8b
The peak current to and from a capacitor 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 current and voltage in a capacitor. The current through a capacitor is given by the formula: , where is the current, is the capacitance, and is the rate of change of voltage.
For an AC circuit, the voltage across the capacitor varies sinusoidally, and the current is proportional to the rate of change of this voltage. The peak current is related to the peak voltage by the formula: , where is the angular frequency, is the capacitance, and is the peak voltage.
Notice that the peak current is directly proportional to the peak voltage. If the peak voltage is doubled, the peak current will also double, assuming the capacitance and frequency remain constant.
Given that the original peak current is 10 mA, doubling the peak voltage will result in a new peak current that is twice the original value.
Conclude that the new peak current can be calculated by multiplying the original peak current by 2. This step completes the solution conceptually.
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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 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. The formula for capacitive reactance (Xc) is Xc = 1/(2πfC), where f is the frequency and C is the capacitance. Understanding this concept is crucial for analyzing how current and voltage relate in capacitive circuits.
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08:02
Capacitors & Capacitance (Intro)
Ohm's Law in AC Circuits
Ohm's Law, which states that V = IR, applies to AC circuits as well, but with modifications to account for reactance. In the context of capacitors, the relationship between peak voltage (V) and peak current (I) can be expressed as I = V/Xc. This means that if the peak voltage is doubled while the frequency remains constant, the peak current will also change proportionally, assuming the reactance remains the same.
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03:12Resistors in AC Circuits
Peak Current and Voltage Relationship
In AC circuits, the peak current and peak voltage are directly related through the impedance of the circuit. For a capacitor, if the peak voltage is increased while keeping the frequency constant, the peak current will increase proportionally, as long as the capacitive reactance does not change. This relationship is essential for predicting how changes in voltage affect current in capacitive systems.
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07:14RMS Current and Voltage
Related Practice
Textbook Question
A capacitor 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 capacitance C?
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Textbook Question
The peak current to and from a capacitor is 10 mA. What is the peak current if the emf frequency is doubled?
Textbook Question
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 kHz?
1
views
Textbook Question
A 20 nF capacitor is connected across an AC generator that produces a peak voltage of 5.0 V. What is the instantaneous value of the emf at the instant when iC = IC?
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Textbook Question
A 20 nF capacitor is connected across an AC generator that produces a peak voltage of 5.0 V. At what frequency f is the peak current 50 mA?