Question

Answer 1

a/ \(\zeta=5.1,5=7,5\left(V\right)\)

\(\dfrac{1}{r}=\dfrac{3}{5r'}\Leftrightarrow r=\dfrac{5r'}{3}=\dfrac{5.0,15}{3}=0,25\left(\Omega\right)\)

b/ \(I=\dfrac{\zeta}{r+\dfrac{R_1R_2}{R_1+R_2}}=\dfrac{70}{17}\left(A\right)\)

\(U_{12}=U_1=U_2=\zeta-I.r=...\left(V\right)\)

\(\Rightarrow P_1=\dfrac{U^2_1}{R_1}=...\left(W\right)\)

c/ \(P_{12}=I^2.R_{12}=\left(\dfrac{\xi}{r+R_{12}}\right)^2.R_{12}=\dfrac{\xi^2}{r^2+2rR_{12}+R_{12}^2}=\dfrac{\xi^2}{\dfrac{r^2}{R_{12}}+2r+R_{12}}\)

\(P_{max}\Leftrightarrow\dfrac{r^2}{R_{12}}+2r+R_{12}\left(min\right)\)

\(\dfrac{r^2}{R_{12}}+2r+R_{12}\ge2\sqrt{\dfrac{r^2}{R_{12}}.R_{12}}+2r=...\)

\("="r^2=R_{12}^2\Leftrightarrow R_{12}=r\Rightarrow R_2=...\left(\Omega\right)\Rightarrow P=...\left(W\right)\)