Question

doua conductoare confectionate din acelasi materiL au lungimile in raport de 1:8. Diametrle sectiunilor sunt in raport de 3:2. cat este raportul rezistentelor acestora?

Answer 1

Se da:
p1=p2
l1/l2=1/8
D1/D2=3/2
R1/R2

Formule:
l1/l2=1/8
8*l1=l2

D1/D2=3/2
2*D1=3*D2

S=πR²
S=πD²/4
D=√4S/π

2*√4*S1/π=3*√4*S2/π
4*4*S1/π=9*4*S2/π
4*S1=9*S2
S2=4*S1/9

[tex] \frac{R1}{R2}=\frac{p1*l1}{S1}/ \frac{p2*l2}{S2}\\ \frac{R1}{R2}= \frac{p1*l1*S2}{S1*p2*l2}\\ \frac{R1}{R2}= \frac{l1* \frac{4*S1}{9} }{S1*8*l1} \\ \frac{R1}{R2}= \frac{l1*4*S1}{9*S1*8*l1}\\ \frac{R1}{R2}= \frac{1}{18} [/tex]