Question

大学电路题目，大神给个过程

Answer 1

I1支路Z1=41.23∠76°

I2支路Z2=11.18∠-63.4°

Z1+Z1=(15+j30)=33.54∠63.43°

I1和I2的并联电路

Z`=Z1//Z2=(10+j40)//(5-j10)

=(10+j40)(5-j10)/[(10+j40)+(5-j10)]

=(50-j100+j200+400)/(15+j30)=(450+j100)/(15+j30)

=461∠12.53°/33.54∠63.43°=13.74∠-50.9°=8.67-j10.66

总Z=10+Z`=18.67-j10.66=21.5∠-29.7°

U10=10∠0°xZ=215∠-29.7°V

I1=10∠0°xZ2/(Z1+Z2)=10∠0°x11.18∠-63.4°/33.54∠63.43°=3.33∠-126.8°

I2=10∠0°xZ1/(Z1+Z2)=10∠0°x41.23∠76°/33.54∠63.43°=12.3∠12.57°

电流源串联10Ω电阻功率PR=10^2x10=1000W

支路1复功率S1=I1^2(10+j40)=111.1+j444.4

支路1复功率S2=I2^2(5-j10)=756.5-j1513

P=1000+111.1+756.5=1867.6≈1868W

Q=-j1513+j444.4=1068.6≈1065Var

基本符合电源总复功率S=U10xI=215∠-29.7°Vx10∠0°=1868-j1065