1.4 Voltage

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1.4 Voltage

As explained briefly in the previous section, to mo ve the electron in a conductor in a particular direction requires some w ork or energy transfer. This work is performed by an e xternal electromotive force (emf), typically represented by the battery in Fig. 1.3. This emf is also kno wn as voltage or potential difference. The voltage vab between two points a and b in an electric circuit is the energy (or work) needed to move a unit charge from b to a; mathematically,

v_{ab} \triangleq \frac{dw}{dq} \tag{1.3}

where w is energy in joules (J) and q is charge in coulombs (C). The voltage vab or simply v is measured in volts (V), named in honor of the Italian physicist Alessandro Antonio Volta (1745–1827), who invented the first voltaic battery. From Eq. (1.3), it is evident that

1 volt = 1 joule/coulomb = 1 newton-meter/coulomb

Thus,

Voltage (or potential difference) is the energy required to move a unit charge from a reference point (−) to another point (+), measured in volts (V).

Figure 1.6 sho ws the v oltage across an element (represented by a rectangular block) connected to points a and b. The plus ( +) and minus (−) signs are used to define reference direction or voltage polarity. The vab can be interpreted in two ways: (1) Point a is at a potential of vab volts higher than point b, or (2) the potential at point a with respect to point b is vab. It follows logically that in general

v_{ab} = -v_{ba} \tag{1.4}

For example, in Fig. 1.7, we ha ve two representations of the same v oltage. In Fig. 1.7(a), point a is +9 V above point b; in Fig. 1.7(b), point b is −9 V above point a. We may say that in Fig. 1.7(a), there is a 9-V voltage drop from a to b or equivalently a 9-V voltage rise from b to a. In other words, a voltage drop from a to b is equivalent to a voltage rise from b to a.

Current and voltage are the tw o basic variables in electric circuits. The common term signal is used for an electric quantity such as a current or a voltage (or even electromagnetic wave) when it is used for conveying

Polarity of voltage vab.

Two equivalent representations of the same voltage vab: (a) Point a is 9 V above point b; (b) point b is −9 V above point a.

Practice Problem 1.3

Historical

Alessandro Antonio Volta (1745–1827), an Italian physicist, in vented the electric battery—which provided the first continuous flow of electricity—and the capacitor.

Born into a noble family in Como, Italy, Volta was performing electrical experiments at age 18. His invention of the battery in 1796 revolutionized the use of electricity. The publication of his work in 1800 marked the beginning of electric circuit theory. Volta received many honors during his lifetime. The unit of voltage or potential difference, the volt, was named in his honor.

Keep in mind that electric current is always through an element and that electric voltage is always across the element or between two points.

information. Engineers prefer to call such v ariables signals rather than mathematical functions of time because of their importance in commu nications and other disciplines. Lik e electric current, a constant v oltage is called a dc voltage and is represented by V, whereas a sinusoidally time-varying voltage is called an ac voltage and is represented by v. A dc voltage is commonly produced by a battery; ac v oltage is produced by an electric generator.