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
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 32, Problema 15
A high-pass RC filter with a crossover frequency of 1000 Hz uses a 100 Ω resistor. What is the value of the capacitor?
Guida verificata passo dopo passo1
Understand the problem: A high-pass RC filter is a circuit that allows signals with frequencies higher than the crossover frequency to pass through while attenuating lower frequencies. The crossover frequency (f_c) is given as 1000 Hz, and the resistor (R) has a value of 100 Ω. We need to find the capacitance (C).
Recall the formula for the crossover frequency of an RC circuit: . Rearrange this formula to solve for the capacitance (C): .
Substitute the given values into the formula: . Ensure that the units are consistent (resistance in ohms, frequency in hertz).
Simplify the denominator: Calculate the product of . This will give the value of the denominator in the capacitance formula.
Finally, compute the capacitance (C) by dividing 1 by the result of the denominator. The unit of capacitance will be in farads (F). If needed, convert the result to microfarads (μF) for practical use by multiplying by .
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Concetti chiave
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High-Pass RC Filter
A high-pass RC filter is an electronic circuit that allows signals with a frequency higher than a certain cutoff frequency to pass through while attenuating signals with lower frequencies. It consists of a resistor (R) and a capacitor (C) arranged in a specific configuration. The cutoff frequency is determined by the values of R and C, and it is the frequency at which the output signal is reduced to 70.7% of the input signal.
Video consigliato:
Percorso guidato
09:15
Example 1
Crossover Frequency
The crossover frequency, also known as the cutoff frequency, is the frequency at which the output voltage of the filter is equal to 70.7% of the input voltage. For a high-pass filter, frequencies above this point are allowed to pass, while those below are attenuated. It is calculated using the formula f_c = 1/(2πRC), where f_c is the crossover frequency, R is the resistance, and C is the capacitance.
Video consigliato:
Percorso guidato
05:08Circumference, Period, and Frequency in UCM
Capacitance Calculation
To find the value of the capacitor in an RC circuit, you can rearrange the formula for the crossover frequency. Given the crossover frequency (f_c) and the resistance (R), the capacitance (C) can be calculated using C = 1/(2πf_cR). This relationship shows how the capacitor's value directly influences the filter's behavior and its ability to pass or block certain frequencies.
Video consigliato:
Percorso guidato
08:02Capacitors & Capacitance (Intro)
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