Alternating Current Analysis 259
Then the currents of the circuit diagram shown in Figure 3.34 are evaluated by the
algebraic addition of the individual contributions of each source (superposition
principle), yielding the following:
i 1 (t) = IA1 + iB1(t)
i 1 (t) = 5 − √
__
2 cos(10 t − 45°) A
i 2 (t) = IA2 + iB2(t)
i 2 (t) = √
__
2 cos(10 t − 45°) A
i 3 (t) = IA3 − iB3(t)
i 3 (t) = 5 − 2 √
__
2 cos(10 t − 45°) A
R.3.66 Let the Thevenin’s impedance as seen across an arbitrary load ZL be ZTH = RTH +
jXTH. Then maximum power is delivered to the load ZL, when ZL = RTH − jXTH
(note that ZL is the complex conjugate of ZTH), as illustrated in Figure 3.37.
Let us evaluate the power delivered (in watts) to the load ZL.
The total impedance of the circuit is given by
ZT = ZTH + ZL = 2 RTH
Then,
I
V
R
TH PIR
TH
2 RL TH
2
and
P
V
R
R
V
R
ZL TH W
TH
TH
TH
TH
24
(^22)
+
−
VTH
ZTH = RTH + j XTH
ZL = RTH − j XTH
FIGURE 3.37
Condition for maximum power transfer to ZL.