Question

Ajutor va rog, nu reusesc sa ii dau nici cum de capat acestei probleme

Answer 1

I₁=E/(R₁+r)

I₂=E/(Rp+r)

P₁=R₁I₁²

P₂=RpI₂²

P₁=P₂<=>R₁E²/(R₁+r)²=RpE²/(Rp+r)²<=>R₁Rp²+R₁r²+2R₁Rp=RpR₁²+Rpr²+2R₁Rp<=>R₁Rp²-Rp(r²+R₁²)+R₁r²=0

Δ=(r²+R₁²)²-4R₁²r²=r⁴+R₁⁴+2R₁²r²-4R₁²r²=r⁴+R₁⁴-2R₁²r²=(r²-R₁²)²

Rp₁,₂=(r²+R₁²±√(r²-R₁²)²)/2R₁=(r²+R₁²±(r²-R₁²))/2R₁

Rp₁=(r²+R₁²+r²-R₁²)/2R₁=r²/R₁=2²/6=4/6=0,66 Ω

Rp₂=(r²+R₁²-r²+R₁²)/2R₁=2R₁²/2R₁=R₁

Rp=Rp₁=R₁R₂/(R₁+R₂)<=>0,66=6R₂/(6+R₂)<=>0,66+0,11R₂=R₂<=>0,66=0,89R₂=>R₂=0,66/0,89≅0,75 Ω