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?
153
views
Ch 32: AC Circuits
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 10
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?
Guida verificata passo dopo passo1
Step 1: Recall the formula for capacitive reactance, which is given by \( X_C = \frac{1}{2 \pi f C} \), where \( X_C \) is the capacitive reactance, \( f \) is the frequency, and \( C \) is the capacitance. This formula relates the frequency and capacitance to the opposition to current flow in a capacitor.
Step 2: Use Ohm's Law for AC circuits, which states \( I = \frac{V}{X_C} \), where \( I \) is the current, \( V \) is the voltage, and \( X_C \) is the capacitive reactance. Rearrange this formula to solve for \( X_C \): \( X_C = \frac{V}{I} \).
Step 3: Substitute the given values for the rms voltage (\( V = 6.0 \; \text{V} \)) and the peak current (\( I_{\text{peak}} = 65 \; \text{mA} \)). Note that the rms current \( I_{\text{rms}} \) is related to the peak current by \( I_{\text{rms}} = \frac{I_{\text{peak}}}{\sqrt{2}} \). Calculate \( I_{\text{rms}} \) first, then use it to find \( X_C \).
Step 4: Once \( X_C \) is determined, use the formula \( X_C = \frac{1}{2 \pi f C} \) to solve for the capacitance \( C \). Rearrange the formula to \( C = \frac{1}{2 \pi f X_C} \). Substitute the frequency \( f = 15 \; \text{kHz} = 15,000 \; \text{Hz} \) and the calculated \( X_C \) into this equation.
Step 5: Perform the calculations to find the value of \( C \). Ensure that the units are consistent throughout the calculation (e.g., convert mA to A and kHz to Hz). The final result will give the capacitance in Farads (F).
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
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 energy in an electric field, measured in farads (F). It is defined as the ratio of the electric charge stored on one plate of the capacitor to the voltage across the plates. In AC circuits, capacitance affects how the capacitor reacts to changing voltages and currents, influencing the overall impedance of the circuit.
Video consigliato:
Percorso guidato
08:02
Capacitors & Capacitance (Intro)
RMS Voltage
RMS (Root Mean Square) voltage is a statistical measure of the magnitude of a varying voltage. It represents the equivalent DC voltage that would deliver the same power to a load. In AC circuits, RMS voltage is crucial for calculating power and current, as it provides a consistent value for analysis, especially when dealing with sinusoidal waveforms.
Video consigliato:
Percorso guidato
07:14RMS Current and Voltage
Peak Current
Peak current refers to the maximum instantaneous current flowing through a circuit during one cycle of an AC waveform. It is important for understanding the behavior of components like capacitors in AC circuits, as it helps determine how much current the capacitor can handle at its maximum charge. The relationship between peak current, RMS voltage, and capacitance is essential for calculating the value of the capacitor.
Video consigliato:
Percorso guidato
07:14RMS Current and Voltage
Pratica correlata
Domanda del libro di testo
The peak current to and from a capacitor is 10 mA. What is the peak current if the emf frequency is doubled?
110
views
Domanda del libro di testo
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)?
108
views
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 kHz?
126
views
Domanda del libro di testo
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?
161
views
Domanda del libro di testo
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?
109
views