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 Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not 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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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 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
You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?
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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
What is the inductance of an inductor whose reactance is 120 Ω at 80.0 Hz?