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Another popular type of capacitor is an electrolytic capacitor . It consists of an oxidized metal in a conducting paste. The main advantage of an electrolytic capacitor is its high capacitance relative to other common types of capacitors. For example, capacitance of one type of aluminum electrolytic capacitor can be as high as 1.0 F. However, you must be careful when using an electrolytic capacitor in a circuit, because it only functions correctly when the metal foil is at a higher potential than the conducting paste. When reverse polarization occurs, electrolytic action destroys the oxide film. This type of capacitor cannot be connected across an alternating current source, because half of the time, ac voltage would have the wrong polarity, as an alternating current reverses its polarity (see Alternating-Current Circuts on alternating-current circuits).

A variable air capacitor ( [link] ) has two sets of parallel plates. One set of plates is fixed (indicated as “stator”), and the other set of plates is attached to a shaft that can be rotated (indicated as “rotor”). By turning the shaft, the cross-sectional area in the overlap of the plates can be changed; therefore, the capacitance of this system can be tuned to a desired value. Capacitor tuning has applications in any type of radio transmission and in receiving radio signals from electronic devices. Any time you tune your car radio to your favorite station, think of capacitance.

A photograph of a device with discrete components is shown. One component is the variable air capacitor. It has two parts, a stator and a rotor. The stator has parallel plates of metal and is fixed to the device. The rotor has parallel plates of metal attached to a shaft. The stator and rotor are arranged in a way that their plates are alternately stacked.
In a variable air capacitor, capacitance can be tuned by changing the effective area of the plates. (credit: modification of work by Robbie Sproule)

The symbols shown in [link] are circuit representations of various types of capacitors. We generally use the symbol shown in [link] (a). The symbol in [link] (c) represents a variable-capacitance capacitor. Notice the similarity of these symbols to the symmetry of a parallel-plate capacitor. An electrolytic capacitor is represented by the symbol in part [link] (b), where the curved plate indicates the negative terminal.

Figure a shows two vertical lines. Figure b shows a vertical line to the left and another, slightly curved vertical line to the right. Figure c shows two vertical lines and an arrow cutting across them diagonally. In all figures, each line is connected to a horizontal line on the outside.
This shows three different circuit representations of capacitors. The symbol in (a) is the most commonly used one. The symbol in (b) represents an electrolytic capacitor. The symbol in (c) represents a variable-capacitance capacitor.

An interesting applied example of a capacitor model comes from cell biology and deals with the electrical potential in the plasma membrane of a living cell ( [link] ). Cell membranes separate cells from their surroundings but allow some selected ions to pass in or out of the cell. The potential difference across a membrane is about 70 mV. The cell membrane may be 7 to 10 nm thick. Treating the cell membrane as a nano-sized capacitor, the estimate of the smallest electrical field strength across its ‘plates’ yields the value E = V d = 70 × 10 −3 V 10 × 10 −9 m = 7 × 10 6 V/m > 3 MV/m .

This magnitude of electrical field is great enough to create an electrical spark in the air.

The figure shows a cell membrane with negative signs on the inner boundary and positive signs on the outer boundary. Chloride ions are outside the cell. Diffusion moves them toward the cell while Coulomb force is shown pointing outwards. Some chloride ions are shown passing through the membrane to the inside. Potassium ions are shown inside the cell. Diffusion moves them out towards the membrane while Coulomb force is shown pointing inwards. Some potassium ions are shown passing the membrane to the outside. Sodium ions are outside the cell. Both Coulomb force and diffusion are shown pointing towards the cell. Some sodium ions are shown within the cell.
The semipermeable membrane of a biological cell has different concentrations of ions on its interior surface than on its exterior. Diffusion moves the K + (potassium) and Cl (chloride) ions in the directions shown, until the Coulomb force halts further transfer. In this way, the exterior of the membrane acquires a positive charge and its interior surface acquires a negative charge, creating a potential difference across the membrane. The membrane is normally impermeable to Na+ (sodium ions).

Visit the PhET Explorations: Capacitor Lab to explore how a capacitor works. Change the size of the plates and add a dielectric to see the effect on capacitance. Change the voltage and see charges built up on the plates. Observe the electrical field in the capacitor. Measure the voltage and the electrical field.

Summary

  • A capacitor is a device that stores an electrical charge and electrical energy. The amount of charge a vacuum capacitor can store depends on two major factors: the voltage applied and the capacitor’s physical characteristics, such as its size and geometry.
  • The capacitance of a capacitor is a parameter that tells us how much charge can be stored in the capacitor per unit potential difference between its plates. Capacitance of a system of conductors depends only on the geometry of their arrangement and physical properties of the insulating material that fills the space between the conductors. The unit of capacitance is the farad, where 1 F = 1 C / 1 V .

Conceptual questions

Does the capacitance of a device depend on the applied voltage? Does the capacitance of a device depend on the charge residing on it?

no; yes

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Would you place the plates of a parallel-plate capacitor closer together or farther apart to increase their capacitance?

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The value of the capacitance is zero if the plates are not charged. True or false?

false

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If the plates of a capacitor have different areas, will they acquire the same charge when the capacitor is connected across a battery?

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Does the capacitance of a spherical capacitor depend on which sphere is charged positively or negatively?

no

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Problems

What charge is stored in a 180.0 - μ F capacitor when 120.0 V is applied to it?

21.6 mC

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Find the charge stored when 5.50 V is applied to an 8.00-pF capacitor.

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Calculate the voltage applied to a 2.00 - μ F capacitor when it holds 3.10 μ C of charge.

1.55 V

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What voltage must be applied to an 8.00-nF capacitor to store 0.160 mC of charge?

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What capacitance is needed to store 3.00 μ C of charge at a voltage of 120 V?

25.0 nF

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What is the capacitance of a large Van de Graaff generator’s terminal, given that it stores 8.00 mC of charge at a voltage of 12.0 MV?

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The plates of an empty parallel-plate capacitor of capacitance 5.0 pF are 2.0 mm apart. What is the area of each plate?

1.1 × 10 −3 m 2

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A 60.0-pF vacuum capacitor has a plate area of 0.010 m 2 . What is the separation between its plates?

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A set of parallel plates has a capacitance of 5.0 µ F . How much charge must be added to the plates to increase the potential difference between them by 100 V?

500 µ C

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Consider Earth to be a spherical conductor of radius 6400 km and calculate its capacitance.

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If the capacitance per unit length of a cylindrical capacitor is 20 pF/m, what is the ratio of the radii of the two cylinders?

1:16

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An empty parallel-plate capacitor has a capacitance of 20 µ F . How much charge must leak off its plates before the voltage across them is reduced by 100 V?

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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