Two resistors

Two resistors 20 Ω and 60 Ω are connected in series and an external voltage of 400 V is connected to them. What are the electrical voltages on the respective resistors? Please comment!

Correct result:

U1 =  100 V
U2 =  300 V

Solution:

R1=20 Ω R2=60 Ω U=400 V  R=R1+R2=20+60=80 Ω  I=U/R=400/80=5 A  U1=I R1=5 20=100 VR_{1}=20 \ Ω \ \\ R_{2}=60 \ Ω \ \\ U=400 \ \text{V} \ \\ \ \\ R=R_{1}+R_{2}=20+60=80 \ Ω \ \\ \ \\ I=U/R=400/80=5 \ \text{A} \ \\ \ \\ U_{1}=I \cdot \ R_{1}=5 \cdot \ 20=100 \ \text{V}
U2=I R2=5 60=300 V   Correctness test:  R1:R2=U1:U2=100:300130.3333 r1=R1/R2=20/60130.3333 r2=U1/U2=100/300130.3333 U=U1+U2U_{2}=I \cdot \ R_{2}=5 \cdot \ 60=300 \ \text{V} \ \\ \ \\ \text{ Correctness test: } \ \\ R_{1}:R_{2}=U_{1}:U_{2}=100:300 \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ r_{1}=R_{1}/R_{2}=20/60 \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ r_{2}=U_{1}/U_{2}=100/300 \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ U=U_{1}+U_{2}



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