Domanda del libro di testo
FIGURE EX32.24 shows voltage and current graphs for an inductor. What is the value of the inductance L?
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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 26
An inductor 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 inductance L?
Guida verificata passo dopo passo1
Step 1: Understand the relationship between the inductive reactance (X_L), the frequency (f), and the inductance (L). The formula for inductive reactance is: , where X_L is the inductive reactance, f is the frequency, and L is the inductance.
Step 2: Recall the relationship between the rms voltage (V_rms), the peak current (I_peak), and the inductive reactance (X_L). The peak current is related to the rms current (I_rms) by: . Then, the rms voltage and rms current are related by: .
Step 3: Calculate the rms current (I_rms) using the given peak current (I_peak = 65 mA). Use the formula: . Substitute the value of I_peak into the equation.
Step 4: Solve for the inductive reactance (X_L) using the formula: . Substitute the values of V_rms (6.0 V) and I_rms (calculated in Step 3) into the equation.
Step 5: Finally, calculate the inductance (L) using the formula: . Substitute the values of X_L (calculated in Step 4) and f (15 kHz) into the equation to find L.
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Concetti chiave
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Inductance
Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. It is measured in henries (H) and is defined as the ratio of the induced electromotive force (emf) to the rate of change of current. Higher inductance values indicate a greater ability to store energy.
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Percorso guidato
12:59
Mutual Induction
RMS Voltage and Peak Current
RMS (Root Mean Square) voltage is a way of expressing the effective value of an alternating current (AC) voltage, which is equivalent to a DC voltage that would deliver the same power. The peak current refers to the maximum instantaneous current flowing through the circuit. In AC circuits, these values are related through the impedance of the circuit, which includes resistance and reactance.
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07:14RMS Current and Voltage
Impedance in AC Circuits
Impedance is the total opposition that a circuit offers to the flow of alternating current and is a combination of resistance and reactance. In inductive circuits, the reactance is frequency-dependent and increases with frequency. The relationship between voltage, current, and impedance is described by Ohm's law, adapted for AC as V = I * Z, where V is voltage, I is current, and Z is impedance.
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08:40Impedance in AC Circuits
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