Question

Pe un circuit paralel, format din R1=10 Ohmi, R2=20 Ohmi, R3=30 Ohmi, se disipa o putere P=1200 W. Ce valoare are puterea disippata pe fiecare dintre rezistoare?

Answer 1

$R_1=10 \ \Omega \\ R_2=20 \ \Omega \\ R_3=30 \ \Omega \\ P=1 \ 200 \ W \\ \boxed{P_1-?} \\ \boxed{P_2-?} \\ \boxed{P_3-?} \\ \bold{Rezolvare:} \\ \boxed{\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}} \ \ \ \ \ \ \ \ \boxed{P=I^2 \cdot R} \\ P_1=I^2 \cdot R_1 \\ P_2=I^2 \cdot R_2 \\ P_3=I^2 \cdot R_3 \\ I^2=\frac{P}{R} \\ \frac{1}{R}=\frac{1}{10 \ \Omega}+\frac{1}{20 \ \Omega}+\frac{1}{30 \ \Omega}=\frac{6}{60 \ \Omega}+\frac{3}{60 \ \Omega}+\frac{2}{60 \ \Omega}$
$\frac{1}{R}=\frac{11}{60 \ \Omega} \Rightarrow 11R=60 \ \Omega \\ R=\frac{60 \ \Omega}{11} \Rightarrow R=5,45 \ \Omega \\ I^2=\frac{1 \ 200 \ W}{5,45 \ \Omega} \Rightarrow I^2=220 \ A^2 \\ P_1=220 \ A^2 \cdot 10 \ \Omega \\ \Rightarrow \boxed{P_1=2 \ 200 \ W}} \\ P_2=220 \ A^2 \cdot 20 \ \Omega \\ \Rightarrow \boxed{P_2=4 \ 400 \ W} \\ P_3=220 \ A^2 \cdot 30 \ \Omega \\ \Rightarrow \boxed{P_3=6 \ 600 \ W}$