Rezolvare
Utilizam formula cunoscuta pentru gruparea generatoarelor in paralel:
[tex]E_p=\dfrac{\sum_{k=1}^n\left(\dfrac{E_k}{r_k}\right)}{\sum_{k=1}^n\left(\dfrac{1}{r_k}\right)}\:\:\:\:(*)[/tex]
In cazul nostru:
[tex]E_p=\dfrac{\dfrac{E_1}{r}+\dfrac{E_2}{r}}{\dfrac{2}{r}}=\dfrac{E_1+E_2}{2}=7\:V\:\boxed{\text{Varianta }\boldsymbol{c}}[/tex]
Demonstratia formulei [tex](*)[/tex]
Fie [tex]I_1,\cdots, I_n[/tex] intensitatile curentilor prin [tex]E_1, \cdots, E_n[/tex], si fie [tex]I[/tex] intensitatea prin ramura principala (nu ne intereseaza ce contine aceasta ramura).
Legea Kirchhoff I: [tex]I=I_1+I_2+\cdots+I_n[/tex]
Legile Kirchhoff II in ochiurile formate de ramurile cu generatorul [tex]k[/tex] si ramura principala: [tex]I_k=\dfrac{E_k-IR}{r_k}\:\:\:\:(k\in 1, 2, 3, \cdots, n)[/tex]
Insumand relatiile date de Kirchhoff II si inlocuind in relatia data de Kirchhoff I, se obtine formula utilizata.
[tex]E_p=\dfrac{\sum_{k=1}^n\left(\dfrac{E_k}{r_k}\right)}{\sum_{k=1}^n\left(\dfrac{1}{r_k}\right)}\:\:\:\:(*)[/tex]
