Question

HEEEELP.......................

Answer 1

Fie r₁ ,r₂,r₃ rezistentele pe ramurile a ,b respectiv AC

R_AC=(r₁+r₂)r₃/(r₁+r₂+2r₃)

R_BD=[2r₁r₂+r₃(r₁+r₂)]/(r₁+r₂+2r₃)

R_BD/R_AC=[2r₁r₂+r₃(r₁+r₂)]/(r₁+r₂+2r₃)/(r₁+r₂)r₃/(r₁+r₂+2r₃)=[2r₁r₂+r₃(r₁+r₂)]/(r₁+r₂)r₃

r₁=ρa/S

r₂=ρb/S=4ρa/3S

r₃=ρ√(a²+b²)/S=ρ√(a²+16a²/9)/S=5ρa/3S

R_BD/R_AC=[2r₁r₂+r₃(r₁+r₂)]/(r₁+r₂)r₃=[2ρa*4ρa/3S*S+5ρa/3S(ρa/S+4ρa/3S)]/5ρa/3S(ρa/S+4ρa/3S)=(8ρ²a²/3S²+35ρ²a²/9S²)/35ρ²a²/9S²=59ρ²a²/9S²/35ρ²a²/9S²=59/35=>R_BD/R_AC=59/35