Unformatted text preview: ly made from metallic alloys and carbon compounds. The circuit | e-Text Main Menu | Textbook Table of Contents | Problem Solving Workbook Contents CHAPTER 2 Basic Laws 29 symbol for the resistor is shown in Fig. 2.1(b), where R stands for the
resistance of the resistor. The resistor is the simplest passive element.
Georg Simon Ohm (1787–1854), a German physicist, is credited
with ﬁnding the relationship between current and voltage for a resistor.
This relationship is known as Ohm’s law. Ohm’s law states that the voltage v across a resistor is directly proportional
to the current i ﬂowing through the resistor.
v∝i (2.2) Ohm deﬁned the constant of proportionality for a resistor to be the resistance, R . (The resistance is a material property which can change if the
internal or external conditions of the element are altered, e.g., if there are
changes in the temperature.) Thus, Eq. (2.2) becomes
v = iR (2.3) which is the mathematical form of Ohm’s law. R in Eq. (2.3) is measured
in the unit of ohms, designated . Thus, The resistance R of an element denotes its ability to resist the ﬂow
of electric current; it is measured in ohms ( ).
We may deduce from Eq. (2.3) that
i + v=0 R=0 so that
1 − = 1 V/A To apply Ohm’s law as stated in Eq. (2.3), we must pay careful
attention to the current direction and voltage polarity. The direction of
current i and the polarity of voltage v must conform with the passive sign
convention, as shown in Fig. 2.1(b). This implies that current ﬂows from
a higher potential to a lower potential in order for v = iR . If current
ﬂows from a lower potential to a higher potential, v = −iR .
Since the value of R can range from zero to inﬁnity, it is important
that we consider the two extreme possible values of R . An element with
R = 0 is called a short circuit, as shown in Fig. 2.2(a). For a short circuit,
v = iR = 0 v v | e-Text Main Menu | Textbook Table of Contents | (a) +
R=∞ − (2.5) showing that the voltage is zero but the current could be anything. In
practice, a short ci...
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