Question

Avem 2 conductoare daca le unim in serie R=50 ohm, daca le unim in paralel R1=12ohm, ce rezistenta are fiecare conductor

Answer 1

Se da:
Rs=50ohm
Rp=12ohm
R1;R2=?ohm

Formule:
Rs=R1+R2⇒R2=Rs-R1

1/Rp=1/R1+1/R2
1/Rp=1/R1+1/(Rs-R1)
1/Rp=(Rs-R1+R1)/[R1(Rs-R1)]
Rp=R1*(Rs-R1)/Rs
Rp*Rs=R1*Rs-R1²
R1²-R1*Rs+Rp*Rs=0

Notam cu x-R1 si rezolvam ecuatia de gradul 2:
x²-50x+600=0
Δ=50²-4*600=100

x1=50-√100/2=20
x2=50+√100/2=30

Avem 2 cazuri posibile: R1'=20ohm, R1''=30ohm, deci:
R2=Rs-R1⇒R2'=50-20=30ohm si R2''=50-30=20ohm

Raspuns: 20 si 30 sau 30 si 20.