Problem: I need to calculate a power balance, to check that i have found the correct currents.
I have found that:
\begin{cases} I_{1}=-2.571 \\ I_{2}=-1.244 \\ I_{4}=1.755 \\ I_{6}=0.42 \end{cases}
The task is to calculate power balance and check it:
I do it using this formula:
$$R_{1} \cdot I_{1}^2+R_{2} \cdot I_{2}^2+R_{3} \cdot I_{2}^2+R_{4} \cdot I_{4}^2+R_{5} \cdot I_{general}^2+R_{6} \cdot I_{6}^2 = E \cdot I_{2}+U_{general}I_{general}$$
\$R_{1} \cdot I_{1}^2+R_{2} \cdot I_{2}^2+R_{3} \cdot I_{2}^2+R_{4} \cdot I_{4}^2+R_{5} \cdot I_{general}^2+R_{6} \cdot I_{6}^2\$ = 727 Watts
Update:
\$U_{general}=-R_{5} \cdot 3A+R_{2} \cdot I_{2}-8+R_{3} \cdot I_{2}+R_{1} \cdot I_{1}=0\$
\$U_{general} = 245.91 Volts\$
- \$E \cdot I_{2}^2 = 12.38 Watt\$ and \$U_{general} \cdot 3=737 Watt\$
Sum of power of sources = \$737+12.38= 749.38\$
- Consumed power = 727 Watts
Given 3% of inaccuracy, which is 22 Watts, I guess that I solved it right, didn't I?
