Se da:
E=12V
r=1Ω
Pext=20W
U=?V
R=?Ω
Rezolvare:
Pext=I²R
Pext=E²R/(R+r)²
(R+r)²=E²R/Pext
R²+2rR+r²=E²R/Pext
R²+2rR+r²-E²R/Pext
R²+(2r-E²/Pext)R+r²=0
La calcule se va rezolva ecuatia de gradul 2
U=I*R
U=E*R/(R+r)
Calcule:
R²+(2*1-12²/20)+1²=0
R²-5,2R+1=0
Δ=23,04 (-5,2²-4*1*1=27,04-4=23,04)
R1=(5,2-√23,04)/2=0,2Ω
R2=(5,2+√23,04)/2=5Ω
U1=12*0,2/(0,2+1)²=1,(6)V
U2=12*5/(5+1)²=1,(6)V