Introduction to Electric Circuits

16 Electric circuit elements

Table 2.1
Material Conductivity (S m -1) Resistivity (11 m)
Silver 6.1 x 107 1.64 x 10 -8
Copper 5.7 x 107 1.75 x 10 -8
Carbon 3 x 104 3.33 • 10 -5
Distilled water 1 • 10 -4 1 • 104
Glass 1 X 10 -12 1 X 1012
Mica 1 x 10-15 1 x 1015
Quartz 1 X 10 -17 1 X 1017

Resistors M series

If a number of resistors are connected as shown in the diagram of Fig. 2.5 they

I

V

R1 I R2 I R3

IR1 IR2 IR3

I

Figure 2.5

are said to be in series. Resistors are in series, therefore, if the same current
flows through each of them. In the diagram of Fig. 2.6, for example, only the
resistors R5 and R 6 are in series with each other. Resistor R~ is in series with the
combination of all the others.

Figure 2.6

I1 R1 l

o > [" I

R2 R5 R6

5

IR4 R7

ti3 R3! I6

t , ~ t! o

By Ohm's law the potential difference across the resistors R1, R2 and R3 in
Fig. 2.5 is given by IRA, IR2 and IRa, respectively. The total potential difference
between the terminals A and B is therefore IR 1 + IR 2 + IR 3 = I[R~ + R 2 + R3].
Although this seems obvious, we have, in fact, anticipated Kirchhoff's voltage
law which will be stated formally in Chapter 3. A single resistor which would
take the same current (I) from the same source (V) would have to have a
resistance of [R 1 + R2 4-R3]. The equivalent resistance (R~q) of the three