只闭合S1,R1与R3串联.
I1=U/(R1+R3) ①
P1=I1²R1= U²R1/(R1+R3)² ②
P3=I1²R3=4W ③
只闭合S2,R2与R3串联.
I2=U/(R2+R3) ④
P2=I2²R3= U²R3/(R2+R3)² ⑤
由②得：R1=P1/I1²
由⑤得：R3=P2/I2²
已知：P1：P2=4:9,I1：I2=2:3
得：R1=R3 ⑥
综合②③⑥式得：P1=P3=4W
P1=U²R1/(R1+R3)²=U²/4R1=4W
U²=16R1 ⑦
P1：P2=4:9 P1=4W
P2=9W
综合⑤⑥⑦式得：P2=U²R3/(R2+R3)²=16R1²/(R2+R1)²=9W
4R1=3(R2+R1)
R1=3R2 ⑧
开关S1,S2,S3,都闭合时,R1与R2并联.
P总=P1‘+P2'=U²/R1 + U²/R2=16R1/R1 + 16R1/(R1/3)=16+48=64W