§ 9-5 Maximum power transfer in the AC case
thZ
LZ
?I
?
??
?
?
?0VV
LLL
ththth
jXRZ
jXRZ
??
??
L
Lth
LL RZZ
VRIp ?
?
?? 2
2
2
The best that XL can do to maximize PL is to make Xth+XL=0
or XL = -Xth.
The load power becomes
2
2
)( Lth
L
L RR
RVp
??
thLthL RVpRRat 4/2m a x ??
?????? thththLLL ZjXRjXRZ
22
2
)XX()RR(
RV
LthLth
L
????
A resistor R,capacitor C,and voltage source V
are all in series,If the average power dissipated by the resistor is
150W and the rms capacitor voltage is 10V,determine R and C.
ts 300c o s100??
70107.70 22 ???RV
143.27.3270 ??I
uFC 71410300 143.2 ???
?7.3215070 2 ??R
R
C
?
?
?
tVs 300c o s100?
i
Example 2:(p175-12)
Solution:
DP:(p175-19) V=2300V,I=25A,PF=0.815(lag).Find (a)P; (b) Q;
(c) ;(d) S; (e) Z._S
Example:( p176-20) Find I and Ps.
5
)(707.0
400
lag
kW
?
?
kV12
i
2
222
)12000(
)400000()4000005(
I
I
?
???
kWP s 4.4114 0 0 0 0 08.475 2 ????
)(.I 2366847?
(a):P=46.9kW; (b),Q=33.3kVar; (c),57.5 35.4oVA;
(d),S=57.5kVA;(e):Z=92 35.4o