The amount of charge stored in a capacitor is the product of the voltage and the capacity. What limits the amount of charge that can be stored on a capacitor? The voltage can be increased, but electric breakdown will occur if the electric field inside the capacitor becomes too large. The capacity can be increased by expanding the electrode areas and by reducing the gap between the electrodes. In general, capacitors that can withstand high voltages have a relatively small capacity. If only low voltages are needed, however, compact capacitors with rather large capacities can be manufactured. One method for increasing capacity is to insert between the conductors an insulating material that reduces the voltage because of its effect on the electric field. Such materials are called dielectrics (substances with no free charges). When the molecules of a dielectric are placed in the electric field, their negatively charged electrons separate slightly from their positively charged cores. With this separation, referred to as polarization, the molecules acquire an electric dipole moment. A cluster of charges with an electric dipole moment is often called an electric dipole.
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Is there an electric force between a charged object and uncharged matter, such as a piece of wood? Surprisingly, the answer is yes, and the force is attractive. The reason is that under the influence of the electric field of a charged object, the negatively charged electrons and positively charged nuclei within the atoms and molecules are subjected to forces in opposite directions. As a result, the negative and positive charges separate slightly. Such atoms and molecules are said to be polarized and to have an electric dipole moment. The molecules in the wood acquire an electric dipole moment in the direction of the external electric field. The polarized molecules are attracted toward the charged object because the field increases in the direction of the charged object.
The proportionality constant σJ is the conductivity of the material. In a metallic conductor, the charge carriers are electrons and, under the influence of an external electric field, they acquire some average drift velocity in the direction opposite the field. In conductors of this variety, the drift velocity is limited by collisions, which heat the conductor.
If the wire in Figure 12 has a length l and area A and if an electric potential difference of V is maintained between the ends of the wire, a current i will flow in the wire. The electric field E in the wire has a magnitude V/l. The equation for the current, using Ohm’s law, is
The quantity l/σJA, which depends on both the shape and material of the wire, is called the resistance R of the wire. Resistance is measured in ohms (Ω). The equation for resistance,
is often written as
where ρ is the resistivity of the material and is simply 1/σJ. The geometric aspects of resistance in equation (20) are easy to appreciate: the longer the wire, the greater the resistance to the flow of charge. A greater cross-sectional area results in a smaller resistance to the flow.
The resistive strain gauge is an important application of equation (20). Strain, δl/l, is the fractional change in the length of a body under stress, where δl is the change of length and l is the length. The strain gauge consists of a thin wire or narrow strip of a metallic conductor such as constantan, an alloy of nickel and copper. A strain changes the resistance because the length, area, and resistivity of the conductor change. In constantan, the fractional change in resistance δR/R is directly proportional to the strain with a proportionality constant of approximately 2.
A common form of Ohm’s law is
where V is the potential difference in volts between the two ends of an element with an electric resistance of R ohms and where i is the current through that element.
Table 2 lists the resistivities of certain materials at room temperature. These values depend to some extent on temperature; therefore, in applications where the temperature is very different from room temperature, the proper values of resistivities must be used to calculate the resistance. As an example, equation (20) shows that a copper wire 59 metres long and with a cross-sectional area of one square millimetre has an electric resistance of one ohm at room temperature.
|*Values very sensitive to purity.|
|1.6 × 10−8|
|1.7 × 10−8|
|2.7 × 10−8|
|1.4 × 10−5|
|4.7 × 10−1|
|2 × 103|
|5 × 1012|
|1 × 1017|
|>1 × 1019|