# 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:

$R_{1}=20 \ Ω \ \\ R_{2}=60 \ Ω \ \\ U=400 \ \text{V} \ \\ \ \\ R=R_{1}+R_{2}=20+60=80 \ Ω \ \\ \ \\ I=U/R=400/80=5 \ \text{A} \ \\ \ \\ U_{1}=I \cdot \ R_{1}=5 \cdot \ 20=100 \ \text{V}$
$U_{2}=I \cdot \ R_{2}=5 \cdot \ 60=300 \ \text{V} \ \\ \ \\ \text{ Correctness test: } \ \\ R_{1}:R_{2}=U_{1}:U_{2}=100:300 \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ r_{1}=R_{1}/R_{2}=20/60 \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ r_{2}=U_{1}/U_{2}=100/300 \doteq \dfrac{ 1 }{ 3 } \doteq 0.3333 \ \\ U=U_{1}+U_{2}$

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