Textbook Question
What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz?
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Ch 31: Alternating Current
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 31, Problem 4b
A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the capacitance C of the capacitor if the current amplitude is 5.30 A?
Verified step by step guidance1
Start by understanding the relationship between the current amplitude (I), voltage amplitude (V), and the capacitive reactance (X_c) in an AC circuit. The formula is: I = V / X_c.
Recall that the capacitive reactance (X_c) is given by the formula: X_c = 1 / (2πfC), where f is the frequency and C is the capacitance.
Rearrange the formula for capacitive reactance to solve for capacitance (C): C = 1 / (2πfX_c).
Substitute the expression for X_c from step 2 into the equation from step 1: I = V / (1 / (2πfC)).
Rearrange the equation from step 4 to solve for C: C = I / (2πfV). Substitute the given values for I, f, and V to find the capacitance.
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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 (Xc) is the opposition that a capacitor offers to the flow of alternating current (AC). It is inversely proportional to the frequency (f) of the AC source and the capacitance (C) of the capacitor, given by the formula Xc = 1/(2πfC). Understanding this concept is crucial for calculating the capacitance when the current amplitude is known.
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Capacitors & Capacitance (Intro)
Ohm's Law for AC Circuits
Ohm's Law in AC circuits relates the voltage amplitude (V), current amplitude (I), and reactance (X) through the formula V = IX. For capacitors, this becomes V = IXc, where Xc is the capacitive reactance. This relationship helps determine the capacitance when the voltage and current amplitudes are given.
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03:12Resistors in AC Circuits
AC Circuit Analysis
AC circuit analysis involves understanding how components like capacitors behave under alternating current. Unlike DC circuits, AC circuits require consideration of phase differences and reactance. Analyzing these circuits involves using complex numbers and phasors to represent voltages and currents, which is essential for solving problems involving capacitors in AC circuits.
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Related Practice
Textbook Question
(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. (b) Compute the reactance of a 2.50-μF capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-μF capacitor?
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Textbook Question
A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?
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Textbook Question
A capacitance C and an inductance L are operated at the same angular frequency. (a) At what angular frequency will they have the same reactance? (b) If L = 5 00 mH and C = 3.50 μF, what is the numerical value of the angular frequency in part (a), and what is the reactance of each element?
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Textbook Question
The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1) v = Vcosωt. The voltage amplitude is V = 45.0 V. What are (a) the root-mean-square potential difference Vrms and (b) the average potential difference Vav between the two terminals of the power supply?
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Textbook Question
A sinusoidal current i = I cosωt has an rms value Irms = 2.10 A. What is the current amplitude?
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