Resistances 80706

The current I = 4A branches into three wires with resistances R1 = 2Ώ, R2 = 5Ώ, R3 = 10Ώ. Calculate the total resistance of the connection and the voltage of the source. How big are the currents in each wire?

Correct answer:

R =  1.25 Ω
U =  5 V
I₁ =  2.5 A
I₂ =  1 A
I₃ =  0.5 A

Step-by-step explanation:

$$\begin{gathered} R_1=2\Omega \\ {R}_2=5\Omega \\ {R}_3=10\Omega \\ I=4\text{A} \\ \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3} \\ R=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}}=\frac{1}{\frac{1}{2}+\frac{1}{5}+\frac{1}{10}}=1.25\Omega \end{gathered}$$

$U=R\cdot I=1.25\cdot 4=5\text{V}$

$I_1=\frac{U}{R_1}=\frac{5}{2}=2.5\text{A}$

$I_2=\frac{U}{R_2}=\frac{5}{5}=1\text{A}$

$$\begin{gathered} I_3=\frac{U}{R_3}=\frac{5}{10}=\frac{1}{2}=0.5=0.5\text{A} \\ \text{ Verifying Solution: } \\ s=I_1+I_2+I_3=2.5+1+0.5=4\text{A} \end{gathered}$$

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