Domanda del libro di testo
For an RC circuit, find an expression for the angular frequency at which VR = ½ ε0. What is VC at this frequency?
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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 42b
What is the peak voltage across the 3.0 μF capacitor?
Guida verificata passo dopo passo1
Step 1: Identify the components in the circuit. The circuit consists of an AC voltage source with a peak voltage of 10 V and a frequency of 200 Hz, connected to three capacitors: 4.0 μF, 3.0 μF, and 6.0 μF. The 3.0 μF and 6.0 μF capacitors are in parallel, and this combination is in series with the 4.0 μF capacitor.
Step 2: Calculate the equivalent capacitance of the parallel combination of the 3.0 μF and 6.0 μF capacitors. For capacitors in parallel, the equivalent capacitance is given by: . Substituting the values: .
Step 3: Calculate the total equivalent capacitance of the circuit. The 9.0 μF equivalent capacitance from Step 2 is in series with the 4.0 μF capacitor. For capacitors in series, the equivalent capacitance is given by: . Substituting the values: .
Step 4: Determine the voltage across the 9.0 μF equivalent capacitance (which includes the 3.0 μF capacitor). The voltage across capacitors in series is divided inversely proportional to their capacitances. Use the formula: . Substituting the values for the total voltage (10 V) and the capacitances, calculate the voltage across the 9.0 μF equivalent capacitance.
Step 5: Calculate the voltage across the 3.0 μF capacitor. Since the 3.0 μF and 6.0 μF capacitors are in parallel, they share the same voltage. The voltage across the 3.0 μF capacitor is equal to the voltage across the 9.0 μF equivalent capacitance calculated in Step 4.
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Concetti chiave
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Capacitance
Capacitance is the ability of a capacitor to store charge per unit voltage. It is measured in farads (F), with common subunits like microfarads (μF). In this circuit, the capacitors have values of 3.0 μF, 4.0 μF, and 6.0 μF, which determine how much charge they can hold when connected to a voltage source.
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Percorso guidato
08:02
Capacitors & Capacitance (Intro)
AC Voltage and Peak Voltage
In alternating current (AC) circuits, voltage varies sinusoidally over time. The peak voltage (E₀) is the maximum voltage reached in one cycle, which in this case is given as 10 V. Understanding peak voltage is crucial for analyzing how capacitors behave in AC circuits, as it influences the charge stored in the capacitors.
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Percorso guidato
07:14RMS Current and Voltage
Series and Parallel Capacitors
Capacitors can be arranged in series or parallel configurations, affecting the total capacitance of the circuit. In this case, the 3.0 μF and 6.0 μF capacitors are in parallel with the 4.0 μF capacitor. The total capacitance for parallel capacitors is the sum of their capacitances, which is essential for calculating the voltage across each capacitor.
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Percorso guidato
09:51Combining Capacitors in Series & Parallel
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