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What are the charge on and the potential difference across each capacitor in FIGURE P26.57?
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Ch 26: Potential and Field
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 26, Problema 54
Find expressions for the equivalent capacitance of (a) N identical capacitors C in parallel and (b) N identical capacitors C in series.
Guida verificata passo dopo passo1
To solve part (a), recall that for capacitors in parallel, the equivalent capacitance is the sum of the individual capacitances. For N identical capacitors, each with capacitance \( C \), the equivalent capacitance \( C_{eq} \) is given by: \( C_{eq} = C + C + \dots + C \) (N terms). This simplifies to \( C_{eq} = N \cdot C \).
For part (b), recall that for capacitors in series, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances. For N identical capacitors, each with capacitance \( C \), the equation becomes: \( \frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{C} + \dots + \frac{1}{C} \) (N terms).
Simplify the series equation: \( \frac{1}{C_{eq}} = \frac{N}{C} \).
Take the reciprocal to find the equivalent capacitance for capacitors in series: \( C_{eq} = \frac{C}{N} \).
Summarize the results: (a) For N capacitors in parallel, \( C_{eq} = N \cdot C \). (b) For N capacitors in series, \( C_{eq} = \frac{C}{N} \).
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Capacitance
Capacitance is the ability of a system to store electric charge per unit voltage. It is measured in farads (F) and is defined as the ratio of the electric charge (Q) stored on a conductor to the potential difference (V) across it. Understanding capacitance is essential for analyzing how capacitors behave in circuits.
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Percorso guidato
08:02
Capacitors & Capacitance (Intro)
Capacitors in Parallel
When capacitors are connected in parallel, the total or equivalent capacitance (C_eq) is the sum of the individual capacitances. This is because each capacitor experiences the same voltage across its terminals, allowing them to store charge independently. The formula for N identical capacitors in parallel is C_eq = N * C, where C is the capacitance of one capacitor.
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Percorso guidato
08:53Parallel Plate Capacitors
Capacitors in Series
In a series configuration, the total capacitance is found using the reciprocal of the sum of the reciprocals of the individual capacitances. This occurs because the charge stored on each capacitor is the same, but the voltage across each capacitor can differ. The formula for N identical capacitors in series is 1/C_eq = N/C, leading to C_eq = C/N.
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Percorso guidato
09:51Combining Capacitors in Series & Parallel
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