26. Capacitors & Dielectrics

Parallel Plate Capacitors

Multiple Choice
One gallon of typical gasoline has 132 MJ of energy. You wish to store that much energy in a parallel-plate capacitor for an electric car. Assume you charge the capacitor using a $120 V$ power source. You can fill the capacitor with any of the materials listed in Table 21.3, but the spacing between plates has to be 0.080 mm. What is the minimum surface area required for the capacitor? This may help to understand challenges in engineering electric cars.
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Multiple Choice
Two circular plates of radius 2cm are brought together so their separation is 5mm. What is the capacitance of these plates?
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Multiple Choice
A 3 F capacitor is given a potential difference across its plates of 10 V. What is the charge built up on its plates? If the source of the potential difference across the plates is removed, but the plates maintain their charge, what is the new potential difference across the capacitor if the distance between the plates is doubled?
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Multiple Choice
What is the smallest possible capacitance of a parallel-plate capacitor with plate area $2500 {cm}^{2}$ separated by a distance $0 . 10 mm$ , if you can fill it with any of the materials listed in Table 21.3?
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Multiple Choice
A parallel plate capacitor consists of two circular plates of radius 12 cm separated by $0 . 23 mm$ . What is the electric field strength inside the capacitor when the plates carry a charge of $14 µ C$ ?
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Multiple Choice
What is the capacitance of a parallel plate capacitor with plate area $2500 {cm}^{2}$ separated by a distance $0.10 mm$ ?
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Multiple Choice
A parallel plate capacitor is charged up using a battery. The battery is then removed, and the plate separation is increased by somebody wearing insulating gloves. What happens to the potential difference between the plates?
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Textbook Question
A parallel-plate air capacitor is to store charge of magnitude $240.0$ pC on each plate when the potential difference between the plates is $42.0$ V.
(a) If the area of each plate is $6.80$ cm², what is the separation between the plates?
(b) If the separation between the two plates is double the value calculated in part (a), what potential difference is required for the capacitor to store charge of magnitude $240.0$ pC on each plate?
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Textbook Question
A $5.00$ - $μ$ F parallel-plate capacitor is connected to a $12.0$ V battery. After the capacitor is fully charged, the battery is disconnected without loss of any of the charge on the plates.
(a) A voltmeter is connected across the two plates without discharging them. What does it read?
(b) What would the voltmeter read if (i) the plate separation were doubled; (ii) the radius of each plate were doubled but their separation was unchanged?
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Textbook Question
A parallel-plate air capacitor of capacitance $245$ pF has a charge of magnitude $0.148$ $μ$ C on each plate. The plates are $0.328$ mm apart.
(a) What is the potential difference between the plates?
(b) What is the area of each plate?
(c) What is the electric field magnitude between the plates?
(d) What is the surface charge density on each plate?
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Textbook Question
The plates of a parallel-plate capacitor are $2.50$ mm apart, and each carries a charge of magnitude $80.0$ nC. The plates are in vacuum. The electric field between the plates has a magnitude of $4.00 \times 10^{6}$ V/m. What is (a) the potential difference between the plates; (b) the area of each plate; (c) the capacitance?
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Textbook Question
Two 2.0 cm×2.0 cm metal electrodes are spaced 1.0 mm apart and connected by wires to the terminals of a 9.0 V battery. The wires are disconnected, and insulated handles are used to pull the plates apart to a new spacing of 2.0 mm. What are the charge on each electrode and the potential difference between them?
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Textbook Question
An isolated capacitor C₁ carries a charge Q₀. Its wires are then connected to those of a second capacitor C₂, previously uncharged. What charge will each carry now? What will be the potential difference across each?
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Textbook Question
(I) What is the capacitance per unit length (F/m) of a coaxial cable whose inner conductor has a 1.0-mm diameter and the outer cylindrical sheath has a 5.0-mm diameter? Assume the space between is filled with air.
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Textbook Question
To get an idea how big a farad is, suppose you want to make a 1-F air-filled parallel-plate capacitor for a circuit you are building. To make it a reasonable size, suppose you limit the plate area to 1.0 cm². What would the gap have to be between the plates? Is this practically achievable?
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