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:

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

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

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