Question

Daca se dubleaza rezistenta unui consumator alimentat de o baterie cu o rezistenta interna de 2 ohmi , tensiunea la bornele bateriei creste de 1,5 ori. Determina valoarea initiala a rezistentei consumatorului.

Answer 1

$R_2=2R_1\\U_2=1,5U_1\\U_1=R_1I_1=>I_1=\frac{U_1}{R_1} \\U_2=R_2I_2=>I_2=\frac{U_2}{R_2} \\I_1=\frac{E}{R_1+r}<=>\frac{U_1}{R_1} =\frac{E}{R_1+r}(1)\\I_2=\frac{E}{R_2+r}<=>\frac{U_2}{R_2} =\frac{E}{R_2+r}(2)\\(1):(2)=>\frac{\frac{U_1}{R_1} }{\frac{U_2}{R_2} }=\frac{\frac{E}{R_1+r}}{\frac{E}{R_2+r}}<=>\frac{U_1R_2}{U_2R_1}=\frac{R_2+r}{R_1+r} <=>\frac{2U_1R_1}{1,5U_1R_1}=\frac{2R_1+r}{R_1+r}<=>\frac{2}{1,5}=\frac{2R_1+r}{R_1+r}<=>2R_1+2r=3R_1+1,5r<=>R_1=0,5r=>R_1=0,5*2=1 \Omega=>R_1=1 \Omega$