Linear Algebra

Topic: Analyzing Networks 73
of the bulb and the other end will be 2 · 25 = 50 volts. This is the voltage drop
across this bulb. One way to think of the above circuit is that the battery is a
voltage source, or rise, and the other components are voltage sinks, or drops,
that use up the force provided by the battery.
The two facts that we need about networks are Kirchhoff’s Laws.
First Law. The flow into any spot equals the flow out.
Second Law. Around a circuit the total drop equals the total rise.
(In the above circuit the only voltage rise is at the one battery, but some circuits
have more than one rise.)
We can use these facts for a simple analysis of the circuit shown below.
There are three components; they might be bulbs, or they might be some other
component that resists the flow of electricity (resistors are drawn as zig-zags ).
When components are wired one after another, as these are, they are said to be
in series.
20 volt
potential
3ohm
resistance
2ohm
resistance
5ohm
resistance
By Kirchhoff’s Second Law, because the voltage rise in this circuit is 20 volts, so
too, the total voltage drop around this circuit is 20 volts. Since the resistance in
total, from start to finish, in this circuit is 10 ohms (we can take the resistance
of a wire to be negligible), we get that the current is (20/10) = 2 amperes. Now,
Kirchhoff’s First Law says that there are 2 amperes through each resistor, and
so the voltage drops are 4 volts, 10 volts, and 6 volts.
Linear systems appear in the analysis of the next network. In this one, the
resistors are not in series. They are instead in parallel. This network is more
like the car’s lighting diagram.
20 volts 12 ohm 8ohm