Lowest voltage

Three resistors with resistors R1 = 10 kΩ, R2 = 20 kΩ, R3 = 30 kΩ are connected in series and an external voltage U = 30 V is connected to them. On which resistor is the lowest voltage?

Final Answer:

U₁ =  5 V
U₂ =  10 V
U₃ =  15 V

Step-by-step explanation:

$$\begin{gathered} U=30\text{V} \\ {R}_1=10\cdot 1000=10000\Omega \\ {R}_2=20\cdot 1000=20000\Omega \\ {R}_3=30\cdot 1000=30000\Omega \\ R=R_1+R_2+R_3=10000+20000+30000=60000\Omega \\ I=\frac{U}{R}=\frac{30}{60000}=\frac{1}{2000}=0.0005\text{A} \\ {U}_1=R_1\cdot I=10000\cdot \frac{30}{60000}=\frac{10000\cdot 30}{60000}=\frac{300000}{60000}=5\text{V} \end{gathered}$$

$U_2=R_2\cdot I=20000\cdot \frac{30}{60000}=\frac{20000\cdot 30}{60000}=\frac{600000}{60000}=10\text{V}$

$$\begin{gathered} U_3=R_3\cdot I=30000\cdot \frac{30}{60000}=\frac{30000\cdot 30}{60000}=\frac{900000}{60000}=15=15\text{V} \\ \text{ Verifying Solution: } \\ {R}_1:R_2:R_3=U_1:U_2:U_3 \end{gathered}$$

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