Two of the most familiar aspects of electricity are its energy and voltage. But energy and voltage are not the same thing. In this chapter, we shall examine the relationship between voltage and electrical energy and begin to explore some of the many applications of electricity.
Electric potential is potential energy per unit charge. The potential difference between points A and B, VB−VA , defined to be the change in potential energy of a charge qmoved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol ΔV .
The voltage between points A and B is \(V=Ed\) where \(d\) is the distance from A to B, or the distance between the plates. In equation form, the general relationship between voltage and electric field is \[E=-\dfrac{\Delta V}{\Delta s},\] where \(\Delta s\) is the distance over which the change in potential, \(\Delta V\), takes place. The minus sign tells us that \(\mathbf{E}\) points in the direction of decreasing potential.) The electric field is said to be the gradient (as in grade or slope)
Electric potential of a point charge is V=kQ/r. Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.
An equipotential line is a line along which the electric potential is constant. An equipotential surface is a three-dimensional version of equipotential lines. Equipotential lines are always perpendicular to electric field lines.The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is called grounding.
A capacitor is a device used to store charge, which depends on two major factors—the voltage applied and the capacitor’s physical characteristics. The capacitance of a parallel plate capacitor when the plates are separated by air or free space. A parallel plate capacitor with a dielectric between its plates has a capacitance that is sensitive to the dielectric constant of the material. The maximum electric field strength when an insulating material break down is called dielectric strength.
Total capacitance in series \(\dfrac{1}{C_{\mathrm{S}}}=\dfrac{1}{C_{1}}+\dfrac{1}{C_{2}}+\dfrac{1}{C_{3}}+\ldots\) Total capacitance in parallel \(C_{\mathrm{p}}=C_{1}+C_{2}+C_{3}+\ldots\) If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.
Thumbnail: The corresponding electric field lines are found by drawing them perpendicular to the equipotentials. Note that these fields are consistent with two equal negative charges.
