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

2.4 Review of some common engineering functions and techniques 109
u (t)
1
u (t – d)
1
Figure2.48
Theunit stepfunction.
t
Figure2.49
Graph ofu(t −d).
d
t
Its graph is shown in Figure 2.48. Note thatu(t) has a discontinuity att = 0. The point
(0, 1) is part of the function defined ont 0. This is depicted by •. The point (0, 0) is
notpartof the function defined ont < 0.We use ◦toillustratethis.
The position of the discontinuity may be shifted.
{ 1 td
u(t−d)=
0 t<d
The graph ofu(t −d) isshown inFigure 2.49.
Engineeringapplication2.18
RLCcircuit
Theinductorisanotherofthethreefundamentalelectroniccomponents.Itisadevice
that is used to store electrical energy in the form of a concentrated magnetic field. It
consistsofatightlywoundcoil,oftenaroundaferromagneticmaterial,whichhelps
to strengthen the magnetic field. It is usually depicted on a circuit diagram as a set
ofloops.Figure2.50showsaresistor,inductorandacapacitorconnectedinparallel.
This is usually known as an RLC circuit. The circuit also contains a switch, which
here is depicted as an arrow connecting two terminals with the switch in the open
position. When the switch is open the voltage v across terminals A and B is zero. If
theswitchisclosedatt = 0thevoltageacrossAandBisV S
,whereV S
isthesupply
voltage. Thus v can bemodelled by the function
{ 0 t<0
v(t) =
t0
V S
This can bewritten,usingthe unit stepfunction, as
v(t) =V S
u(t)
+
A
V S
–
L R C
B
Figure2.50
RLCcircuit.