CHAP. 4]

47

ANALYSIS METHODS

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.

Fig. 4-15

4.10

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

2 #

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.

Fig. 4-16

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.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An