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In FIGURE EX28.30, what is the value of the potential at points 1 and 2?
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Ch 28: Fundamentals of 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 28, Problema 32
Show that the product RC has units of s.
Guida verificata passo dopo passo1
Start by identifying the components of the product RC. Here, R represents resistance, and C represents capacitance. Resistance (R) is measured in ohms (Ω), and capacitance (C) is measured in farads (F).
Express the units of resistance (Ω) in terms of base SI units. Resistance is defined as voltage divided by current, so 1 Ω = 1 V / 1 A. Using the definitions of voltage (V = J/C) and current (A = C/s), we can rewrite 1 Ω as 1 (J/C) / (C/s) = 1 (kg·m²/s³·A) / (A·s) = 1 kg·m²/(s³·A²).
Express the units of capacitance (F) in terms of base SI units. Capacitance is defined as charge per unit voltage, so 1 F = 1 C / 1 V. Using the definition of voltage (V = J/C), we can rewrite 1 F as 1 C / (J/C) = 1 C² / J = 1 C² / (kg·m²/s²) = 1 s⁴·A² / (kg·m²).
Multiply the units of resistance (R) and capacitance (C) together. Substituting the derived units: (kg·m²/s³·A²) × (s⁴·A² / kg·m²) = s.
Conclude that the product RC has the units of seconds (s), as shown by the dimensional analysis.
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Resistance (R)
Resistance is a measure of the opposition to the flow of electric current in a circuit, measured in ohms (Ω). One ohm is defined as the resistance that allows one volt (V) to produce one ampere (A) of current. Understanding resistance is crucial for analyzing how it affects the time constant in RC circuits.
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05:25
Resistivity & Resistors in Circuits
Capacitance (C)
Capacitance is the ability of a system to store an electric charge, measured in farads (F). One farad is defined as the capacitance that allows one coulomb (C) of charge to build up with a potential difference of one volt (V). The capacitance value is essential for determining how quickly a capacitor charges or discharges in an RC circuit.
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08:02Capacitors & Capacitance (Intro)
Time Constant (τ)
The time constant (τ) in an RC circuit is the product of resistance (R) and capacitance (C), expressed as τ = RC. It represents the time required for the voltage across the capacitor to reach approximately 63.2% of its final value during charging or to fall to about 36.8% during discharging. The units of τ are seconds (s), indicating that the product RC must also have units of seconds.
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08:59Phase Constant of a Wave Function
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