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 answer:

U₁ =  100 V
U₂ =  300 V

Step-by-step explanation:

$$\begin{gathered} R_1=20\Omega \\ {R}_2=60\Omega \\ U=400\text{V} \\ R=R_1+R_2=20+60=80\Omega \\ I=U/R=400/80=5\text{A} \\ {U}_1=I\cdot R_1=5\cdot 20=100\text{V} \end{gathered}$$

$$\begin{gathered} U_2=I\cdot R_2=5\cdot 60=300=300\text{V} \\ \text{ Verifying Solution: } \\ {R}_1:R_2=U_1:U_2 \\ {r}_1=R_1/R_2=20/60=\frac{1}{3}\doteq 0.3333 \\ {r}_2=U_1/U_2=100/300=\frac{1}{3}\doteq 0.3333 \\ U=U_1+U_2 \end{gathered}$$

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