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

72 Chapter 2 Engineering functions
Note that the voltage is a linear polynomial function with I as the independent
variable.
This equation is only valid for a finite range of currents. If too much voltage is
appliedtotheresistor,thenthecurrentflowingthroughtheresistorbecomessufficient
forthe resistortooverheat and breakdown.
Engineeringapplication2.5
Anon-idealvoltagesource
An ideal voltage source has zero internal resistance and its output voltage,V, is independent
of the load applied to it; that is,V remains constant, independent of the
current it supplies. It is called an ideal voltage source because it is difficult to create
such a source in practice; it is in effect an abstraction that is useful when developing
engineering models of real electronic systems. A non-ideal voltage source has
aninternal resistance. Due tothis internal resistance, the output voltage from such a
source is reduced when current is drawn from the source. The voltage reduction increasesasmorecurrentisdrawn.Figure2.18showsanon-idealvoltagesource.Itis
modelledasanidealvoltagesourceinserieswithaninternalresistorwithresistance
R s
. The output voltage of the non-ideal voltage source is v o
while v R
is the voltage
drop across the internal resistor andiis the load current. Using Kirchhoff’s voltage
law,
V=v R
+v o
and hence by Ohm’s law,
V =iR s
+v o
v o
=V−iR s
Note thatV and R s
are constants and so the output voltage is a linear polynomial
function with independent variable i. The equation gives the output voltage across
theloadasafunctionofthecurrentthroughtheload.Theoutputcharacteristicforthe
non-idealvoltagesourceisobtainedbyvaryingtheloadresistorR L
andisplottedin
Figure2.19.Noticethattheoutputvoltageofthenon-idealvoltagesourcedecreases
as the load current increases and is equal in value to the ideal voltage source only
when there isno load current.
V
+
–
R s
v R
v o
i
R L
v o
V
gradient = –R s
i
non-ideal voltage source
Figure2.18
Anon-ideal voltage sourceconnected to aload
resistor,R L .
Figure2.19
Output characteristic ofanon-ideal
voltage source.