Introduction to Electric Circuits

14 Electric circuit elements

v = nI (2.3)

where R is the constant of proportionality and is called the resistance of the
conducting material. This is known as Ohm's law.
Rearranging Equation (2.3), we obtain the defining equation R = VII and we
note that the unit of resistance is the unit of voltage divided by the unit of
current, i.e. the volt per ampere. This is called the ohm, symbol D, in honour of
Georg Ohm (1787-1854), a German scientist. Materials which obey Ohm's law
are known as linear or ohmic materials.
Virtually all devices and equipment have inherent resistance. A circuit
element designed specifically to have resistance is called a resistor. There are
two circuit symbols commonly used for resistance and either is perfectly
acceptable. These are shown in Fig. 2.3 together with the characteristic graph.

I R V

+'~N~"

"*v =

I +~ R

~ i'--

V 0 I

Figure 2.3

The point of entry of the current in a resistor is always positive with respect to

the point of exit so far as potential difference is concerned.

Example 2.4

Find the unknown quantities in the diagrams of Fig. 2.4.

Figure 2.4

A , R B A 5A r'~ lf~ ~ B A 2D I B

5A "- l__. I -6V "-' ' VB _6V [ I -3V

10V V

(a) (b) (c)

Solution

(a) Using Ohm's law we have that R = VII = 10/5 = 2 D

(b) Again from V = IR we see that V (the voltage across the

resistor) = 5 x 1 = 5 V. Since the current enters end A, it is at a higher

potential than end B, so VB = VA -- 5 = --6 -- 5 = --11 V

(c) Since end B is at a higher potential than end A, the current must enter end

B. The potential difference across the resistor is 3 V so that

I = V/R = 3/2 - 1.5 A, flowing from right to left through the resistor.