082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

48 Chapter 1 Review of algebraic techniques
This situation is likely to occur in a circuit problem in electronics. There are
two options for labelling the current flow direction, and these are summarized in
Figure 1.6.
1 A
2 A
1 A
2 A
3 A I 4 3 A I 4 Figure1.6
Two different ways ofdefining the
Branch 4
Branch 4 currentdirection in Branch4.
1+3−2−I 4
=0 1+3−2+I 4
=0
I 4
=2 I 4
=−2
Note that the two solutions are both correct butI 4
= −2 has a negative sign, which
simply indicates that the current flows in the opposite direction to the arrow drawn
ontheright-handdiagram.Itdoesnotmatterwhichwayroundthearrowismarked,
as long as weobserve the sign.
Engineeringapplication1.9
Kirchhoff’svoltagelaw
Kirchhoff’s voltage law, often abbreviated to KVL, provides another of the fundamental
equations for analysing electrical circuits. The law states that the sum of the
voltages around a closed loop equals zero. It is often written down in the form of a
summation, as follows:
N∑
V k
=0
k=1
For the circuit shown in Figure 1.7 there are three possible loops to which we
could apply KVL.
V d
V a
V c
V b
V e
Figure1.7
A simple circuitto illustrate Kirchhoff’svoltage law.
In this example an ideal voltage source and resistors are used, although any components
could be substituted as KVL applies universally. Note that we ‘walk around’