Legate in serie:
E_s=3•E
r_s=3•r
[tex] I_1=\frac{E_s}{R+r_s}[/tex]
Legate in paralel:
E_p=E
r_p=r/3
[tex]I_2=\frac{E_p}{R+r_p}[/tex]
Dar I1=I2 =>
[tex] \frac{E_s}{R+r_s}=\frac{E_p}{R+r_p}[/tex]
[tex]\frac{3E}{R+3r}=\frac{E}{R+\frac{r}{3}}[/tex]
[tex]\frac{3}{R+3r}=\frac{1}{R+\frac{r}{3}}[/tex]
[tex]R+3r=3(R+\frac{r}{3})[/tex]
[tex] R+3r=3R+r[/tex]
[tex]2r=2R[/tex]
Deci R=r
