Geoscience Reference
In-Depth Information
Voltage applied = Sum of voltage drops
E
A
=
E
1
+
E
2
+
E
3
where
E
A
is the voltage applied, and
E
1
,
E
2
, and
E
3
are voltage drops.
Another way of stating Kirchhoff's law is that the algebraic sum of the instantaneous emf values
and voltage drops around any closed circuit is zero. Through the use of Kirchhoff's law, circuit
problems can be solved that would be difficult and often impossible with only knowledge of O h m's
law. When Kirchhoff's law is properly applied, an equation can be set up for a closed loop and the
unknown circuit values may be calculated.
11.7.6.7 Polarity of Voltage Drops
When a voltage drop occurs across a resistance, one end must be more positive or more negative
than the other end. The polarity of the voltage drop is determined by the direction of current flow. In
the circuit shown in Figure 11.34, the current is seen to be flowing in a counterclockwise direction
due to the arrangement of the battery source (E). Notice that the end of resistor
R
1
into which the
current flows is marked negative (-). The end of
R
1
at which the current leaves is marked positive
(+). These polarity markings are used to show that the end of
R
1
into which the current flows is at
a higher negative potential than is the end of the resistor from which the current leaves. Point A is
thus more negative than point B.
Point C, which is at the same potential as point B, is labeled negative. This indicates that point C,
although positive with respect to point A, is more negative than point D. To say that a point is posi-
tive (or negative), without stating what it is positive (or negative) with respect to, has no meaning.
Kirchhoff's voltage law can be written as an equation as shown below:
E
a
+
E
b
+
E
c
+ …
E
n
= 0
(11.30)
where
E
a
,
E
b
, etc. are the voltage drops and emf values around any closed circuit loop.
■
EXAMPLE 11.31
Problem:
Three resistors are connected across a 60-volt source. What is the voltage across the third
resistor if the voltage drops across the first two resistors are 10 volts and 20 volts?
Solution:
First, draw a diagram like the one shown in Figure 11.35. Next, assume a direction of cur-
rent as shown. Using this current, place the polarity markings at each end of each resistor and on the
terminals of the source. Starting at point A, trace around the circuit in the direction of current flow,
+
I
D
R
2
-
C
+
E
+
B
-
R
1
I
-
A
FIGURE 11.34
Polarity of voltage drops.
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