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A series circuit has resistances connected one aft er the
other, so the current passing through each resistance is the
same through each resistance. Adding more resistances to a
series circuit will cause a decrease in the current available in
the circuit and a reduction of the voltage available for each
individual resistance. Since power is determined from the
product of the current and the voltage (P = IV), adding more
lamps to a series circuit will result in dimmer lights. Perhaps
you have observed such a dimming when you connected two
+ – or more strings of decorating lights, which are oft en con-
nected in a series circuit. Another disadvantage to a series
Dry Electron current
cell circuit is that if one bulb burns out, the circuit is broken and
all the lights go out.
In the parallel electric circuit, the current has alternate
FIGURE 6.38 A parallel electric circuit.
branches to follow, and the current in one branch does not aff ect

the current in the other branches. The total current in the paral-
resistance. In symbols, the effect of wiring resisters in parallel is

lel circuit is therefore equal to the sum of the current fl owing
1 _ _ _ _ in each branch. Adding more resistances in a parallel circuit
1
1
1

= + +

R R R R results in three major effects that are characteristic of all parallel
1
2
3
total
equation 6.11 circuits:
1. an increase in the current in the circuit;
EXAMPLE 6.12 2. the same voltage is maintained across each resistance; and
3. a lower total resistance of the entire circuit.
Assume the three resistances in example 6.11 are now connected in

parallel. (A) What is the combined resistance? (B) What is the current The total resistance is lowered since additional branches provide
in the overall circuit? (C) What is the current through each resistance? more pathways for the current to move.
SOLUTION
HOUSEHOLD CIRCUITS
A. The total resistance can be found from equation 6.11, and Household wiring is a combination of series and parallel cir-

1 _ 1 _ _ 1 _ cuits (Figure 6.39). Th e light fixtures in a room, for example, are
1
= + +

R R R R wired in parallel, and you can use just one light or all the lights
total 1 2 3
_ 1 _ _ at the same time. A switch, however, is wired in series with the
1
1
= + +

12 Ω 8 Ω 24 Ω light fixtures, as is the fuse or circuit breaker in the circuit.
Each appliance connected to such a parallel circuit has
_ _ _
3
1
2
= + + the same voltage available to do work, and each appliance
24 Ω 24 Ω 24 Ω
draws current according to its resistance. This means that as

1 _ _
6
= additional appliances are turned on or plugged in, additional

R 24 Ω
total current fl ows through the circuit. This means you can turn on

6 × R = 1 × 24 Ω
total the lights and draw 1 amp, then start your 1,200 W blow dryer
24 Ω
_

R = and draw 10 more amps for a total of 11 amps from the same
total 6
circuit. Can you add still more appliances to the same circuit
= 4 Ω when it already has this load? The answer to this question will

B. depend on what else you want to add (how many amps?) and
V _ on the preset load your fuse or circuit breaker will accept before
I =
R breaking the circuit.
_ Without the “guard” role of fuses and circuit breakers,
12 V
=
4 Ω you could add more and more appliances to a circuit and pull

more and more amps. The current could reach high enough
= 3 A
levels to cause overheating and possibly a fire. A fuse or cir-

C.
cuit breaker in the circuit is used to disconnect the circuit if it
V _ V _ V _

I = I = I = reaches the preset value, usually 15 or 20 amps. A fuse is a
3
1
2
R R R disposable, screw-in device that contains a short piece of
3
2
1
_ _ _
12 V
12 V
12 V
= = = metal with a high resistance and low melting point. When
12 Ω 8 Ω 24 Ω
the current through the circuit reaches the preset rating, say
= 1 A = 1.5 A = 0.5 A 15 amps, the short metal strip melts. This gap opens the circuit

just like a switch for the whole circuit. The circuit breaker has

168 CHAPTER 6 Electricity 6-30