Page 55 - Schaum's Outline of Theory and Problems of Electric Circuits

ANALYSIS METHODS
44
Finally, these powers are divided between the individual resistances as follows: [CHAP. 4

6 7
P 12
¼ ð81Þ¼ 27 W P 7
¼ ð27Þ¼ 15:75 W
12 þ 6 7 þ 5
12 5
P 6
¼ ð81Þ¼ 54 W P 5
¼ ð27Þ¼ 11:25 W
12 þ 6 7 þ 5

4.8 SUPERPOSITION

A linear network which contains two or more independent sources can be analyzed to obtain the
various voltages and branch currents by allowing the sources to act one at a time, then superposing the
results. This principle applies because of the linear relationship between current and voltage. With
dependent sources, superposition can be used only when the control functions are external to the network
containing the sources, so that the controls are unchanged as the sources act one at a time. Voltage
sources to be suppressed while a single source acts are replaced by short circuits; current sources are
replaced by open circuits. Superposition cannot be directly applied to the computation of power,
because power in an element is proportional to the square of the current or the square of the voltage,
which is nonlinear.
As a further illustration of superposition consider equation (7) of Example 4.4:

11 21 31
I ¼ V 1 þ V 2 þ V 3
1
R R R
which contains the superposition principle implicitly. Note that the three terms on the right are added
to result in current I 1 . If there are sources in each of the three meshes, then each term contributes to the
current I 1 . Additionally, if only mesh 3 contains a source, V 1 and V 2 will be zero and I 1 is fully
determined by the third term.

EXAMPLE 4.7 Compute the current in the 23-
resistor of Fig. 4-11(a) by applying the superposition principle.
With the 200-V source acting alone, the 20-A current source is replaced by an open circuit, Fig. 4-11(b).

Fig. 4-11