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146 ⏐⏐⏐ SERIES CIRCUITS S
E
(a)
–
E
+
E
+
–
R L
–
E
+
– E +
POWER SUPPLY
(a) (b)
FIG. 5.51
(a) Sources of dc voltage; (b) equivalent circuit.
R int
I L = 0
E
(b)
+
V NL = E
sider the effects of the internal resistance, the output voltage will be E
volts only when no-load (IL � 0) conditions exist. When a load is connected
[Fig. 5.52(c)], the output voltage of the voltage source will
decrease due to the voltage drop across the internal resistance.
By applying Kirchhoff’s voltage law around the indicated loop of
Fig. 5.52(c), we obtain
E � ILRint � VL � 0
or, since E � VNL we have V NL � I LR int � V L � 0
and VL � VNL � ILRint (5.13)
If the value of Rint is not available, it can be found by first solving for
Rint in the equation just derived for VL; that is,
Rint �� VNL � VL � � �
I
VNL
� � �
I
ILRL �
I
L
and Rint � � (5.14)
VNL
� � RL I
A plot of the output voltage versus current appears in Fig. 5.53 for
the dc generator having the circuit representation of Fig. 5.51(b). Note
that any increase in load demand, starting at any level, causes an additional
drop in terminal voltage due to the increasing loss in potential
across the internal resistance. At maximum current, denoted by I FL, the
L
+
–
L
Rint + –
FIG. 5.52
Voltage source: (a) ideal, R int � 0 �; (b) determining V NL; (c) determining R int .
–
IL E
(c)
L
R int
E
V L
+
–
I L
+
–
R L