Fig. 4-15, where it is evident that the resistors R1 ; R2 ; . . . ; Rn can be connected one at a time, and the resulting current and power readily obtained. If this were attempted in the original circuit using, for example, network reduction, the task would be very tedious and time-consuming.
MAXIMUM POWER TRANSFER THEOREM
At times it is desired to obtain the maximum power transfer from an active network to an external load resistor RL . Assuming that the network is linear, it can be reduced to an equivalent circuit as in Fig. 4-16. Then I¼
V0 R 0 þ RL
and so the power absorbed by the load is V 02 RL V 02 PL ¼ 0 ¼ 2 4R 0 ðR þ RL Þ
R 0 RL 1 R 0 þ RL
It is seen that PL attains its maximum value, V 02 =4R 0 , when RL ¼ R 0 , in which case the power in R 0 is also V 02 =4R 0 . Consequently, when the power transferred is a maximum, the eﬃciency is 50 percent.
It is noted that the condition for maximum power transfer to the load is not the same as the condition for maximum power delivered by the source. The latter happens when RL ¼ 0, in which case power delivered to the load is zero (i.e., at a minimum).
Solved Problems 4.1
Use branch currents in the network shown in Fig. 4-17 to ﬁnd the current supplied by the 60-V source.
Published on May 10, 2013