Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo

Giancoli Douglas 5th edition

Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage

Problema 98a

Capitolo 23, Problema 98a

In lightning storms, the potential difference between the Earth and the bottom of the thunderclouds can be as high as 35,000,000 V. The bottoms of thunderclouds are typically 1500 m above the Earth, and can have an area of 110 km². Modeling the Earth–cloud system as a huge capacitor, calculate the capacitance of the Earth–cloud system,

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Model the Earth-cloud system as a parallel plate capacitor. The capacitance of a parallel plate capacitor is given by the formula:

C = \frac{ε}{d} \cdot A

, where

ε

is the permittivity of free space (

ε = 8.85 \times 10^{-12} F / m

A

is the area of the plates, and

d

is the separation between the plates.

Convert the area of the thunderclouds from square kilometers to square meters. Since

1 km ² = 10^{6} m ²

, multiply

110 km ²

10^{6}

to get the area in square meters.

Substitute the values into the capacitance formula. Use

ε = 8.85 \times 10^{-12} F / m

, the converted area

A

, and the separation distance

d = 1500 m

Simplify the expression to calculate the capacitance. Ensure that the units are consistent throughout the calculation, and the result will be in farads (F).

Interpret the result. The capacitance of the Earth-cloud system represents the ability of this system to store charge for a given potential difference.

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Capacitance

Capacitance is a measure of a capacitor's ability to store electric charge per unit voltage. It is defined as the ratio of the electric charge stored (Q) to the potential difference (V) across the capacitor, expressed as C = Q/V. In the context of the Earth-cloud system, capacitance can be modeled using the area of the cloud and the distance to the Earth, allowing us to understand how much charge can be stored given a specific voltage.

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Percorso guidato

08:02

Capacitors & Capacitance (Intro)

Electric Field

The electric field (E) is a vector field that represents the force per unit charge experienced by a positive test charge placed in the field. It is related to the potential difference and the distance over which it acts, given by E = V/d. In the case of the Earth-cloud system, the electric field can be calculated using the potential difference between the cloud and the Earth, which helps in understanding the forces at play during a lightning storm.

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Percorso guidato

03:16

Intro to Electric Fields

Area and Distance in Capacitors

In capacitor theory, the capacitance is influenced by the area of the plates and the distance between them. For parallel plate capacitors, capacitance increases with larger plate area and decreases with greater separation. In the Earth-cloud model, the area of the thundercloud and the height above the Earth are critical parameters that determine the effective capacitance, impacting the system's ability to store charge and the potential for lightning discharge.

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Percorso guidato

06:13

Intro to Capacitors

Pratica correlata

Domanda del libro di testo

A parallel-plate capacitor with plate area 2.0 cm² and air-gap separation 0.50 mm is connected to a 12-V battery, and fully charged. The battery is then disconnected. What is the charge on the capacitor?

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Domanda del libro di testo

Capacitors can be used as “electric charge counters.” Consider an initially uncharged capacitor of capacitance C with its bottom plate grounded and its top plate connected to a source of electrons. If N electrons flow onto the capacitor’s top plate, show that the resulting potential difference V across the capacitor is directly proportional to N.

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Domanda del libro di testo

A parallel-plate capacitor with plate area 2.0 cm² and air-gap separation 0.50 mm is connected to a 12-V battery, and fully charged. The battery is then disconnected. The plates are now pulled to a separation of 0.85 mm. What is the charge on the capacitor now?

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