Question

Într-un circuit simplu, tensiunea la bornele bateriei este 3 V. Mărind rezistența exterioară de 3 ori, tensiunea la borne crește cu 20 \%. T.e.m. a bateriei este:
A) 4,5 V
B) 5,5 V
C) 3,7 V
D) 3,2 V
E) 5 V
F) 4 V

Answer 1

[tex]Se~da:\\ \\ U_1=3V\\ \\ R_2=3\times R_1\\ \\ U_2=1,2\times U_1\\ \\ E=?V\\ \\ \\[/tex]


[tex]Formule:\\ \\ U_2=I_2\times R_2\\ \\ U_2=\frac{E\times R_2}{R_2+r}\\ \\ R_2+r=\frac{E\times R_2}{U_2}\\ \\ r=\frac{E\times R_2}{U_2}-R_2\\ \\ \\[/tex]


[tex]U_1=I_1\times R_1\\ \\ U_1=\frac{E\times R_1}{R_1+r}\\ \\ R_1+r=\frac{E\times R_1}{U_1}\\ \\ r=\frac{E\times R_1}{U_1}-R_1\\ \\ \\[/tex]


[tex]\frac{E\times R_2}{U_2}-R_2=\frac{E\times R_1}{U_1}-R_1\\ \\ \frac{E\times R_2-U_2\times R_2}{U_2}=\frac{E\times R_1-U_1\times R_1}{U_1}\\ \\ E\times R_1\times U_2-U_1\times R_1\times U_2=E\times R_2\times U_1-U_2\times R_2\times U_1\\ \\[/tex]

[tex]1,2 \times E\times R_1\times U_1-1,2 \times U_1\times R_1\times U_1=\\ =3\times E\times R_1\times U_1-3,6\times U_1\times R_1\times U_1\\ \\ 0,4\times E-0,4\times U_1=E-1,2\times U_1\\ \\[/tex]

[tex]0,6\times E=0,8\times U_1\\ \\ E=\frac 43\times U_1\\ \\ \\ Calcule:\\ \\ E=\frac 43\times 3=4V\\ \\ \\ Raspuns:~F). [/tex]