Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

12.4 Electrical Circuits and Components 357

volume in a radio. A resistor dissipates heat as electric current flows through it. The amount of

the heat dissipated depends on the magnitude of the resistor and the amount of the current that

is passing through the resistor.

Similar to a constant flow of water in a series of pipes of varying size, the electric current

flowing through a series of elements in an electric circuit is the same (constant). Moreover, for

a circuit that has elements in a series arrangement, the following is true:

• The voltage drop across each element can be determined using Ohm’s law.


• The sum of the voltage drop across each element is equal to the total voltage supplied to the
  circuit.


• The total resistance is the sum of resistance in the circuit.

For resistors in series, the total equivalent resistance

is equal to the sum of the individual resistors, as shown in

Figure 12.10.

(12.5)

One of the problems with a circuit that has elements

in a series arrangement is that if one of the elements fails,

that failure prevents the current from flowing through

other elements in the circuit; thus the entire circuit fails.

You may have experienced this problem with a series of

light bulbs in a string of Christmas tree lights. In a series

arrangement, when one light fails, the current to other lights stops, resulting in all of the lights

being off.

Example 12.4 Determine the total resistance and the current flowing in the circuit shown in Figure 12.11.

RtotalR 1 R 2 R 3 R 4 R 5

R 1 R 2

R 5 R 4

R 3





■Figure 12.10

Resistors in series,

RtotalR 1 R 2 R 3 R 4 R 5.





9 V

R 1 = 3 

R 3 = 9 

R 2 = 7 

■Figure 12.11 The circuit for Example 12.4.

The light bulbs are connected in a series arrangement; therefore, the total resistance is

given by

We can now use Ohm’s law to determine the current flowing through the circuit.

I

V

Rtotal



9

19

0.47 A0.5 A

RtotalR 1 R 2 R 3  3  7  9  19 

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