Question

串并联电路电阻,电压（电流）分配,功率分配的推导

Answer 1

串：

R=R1+R2 串联电路总电阻值等于各电阻值之和

R=U/I

}R=U1+U2/I }R=U1/I +U2/I =R1+R2

U=U1+U2 ∵I=I1=12

U1/U2=R1/R2

U=IR→U1/U2=I1R1/I2R2 ∵ I=I1=I2 ∴U1/U2=R1/R2

P1/P2=R1/R2

P=I²R P1/P2=I²R1/I²R2 ∵I=I1=I2 ∴ P1/P1=R1/R2

并

1/R=1/R①+1/R②

∵R=U/I

U=U1=U2

∴1/R=U/I1+I2

1/R=U/I1+U/I2

1/R=1/R①=1/R②

I1/I2=R1/R2

U=I1R1=I2R2

I1/12=R2/R1

P1/P2=R2/R1

∵P=U²/R

P1/P2=U²/R1/U²/R2=R2/R1