A resistor is constructed as a hollow cylinder with inner and outer radii ra=0.5 cm , rb=1.0 cm respectively and resistivity ρ =3.5× 10- 5 Ω m . The resistance of the configuration for the length of 5 cm cylinder is × 10- 3 Ω .

Question

A resistor is constructed as a hollow cylinder with inner and outer radii ra=0.5 cm , rb=1.0 cm respectively and resistivity ρ =3.5× 10- 5 Ω m . The resistance of the configuration for the length of 5 cm cylinder is × 10- 3 Ω . (A)  text7.42 (B)  text10.56 (C)  text14.38 (D)  text16.48

Tardigrade Admin · Accepted Answer

Given. l=5 cm =5 × 10-2 m ρ=3.5 × 10-5 Ω m A=π(1 × 10-4-0.25 × 10-4) =0.75 π × 10-4 m 2 =7.5 π × 10-5 m 2 ∴ R=(ρ l/A)=(3.5 × 10-5 × 5 × 10-2/7.5 π × 10-5) =7.42 × 10-3 Ω

Q. A resistor is constructed as a hollow cylinder with inner and outer radii $r_{a} = 0.5 c m$ , $r_{b} = 1.0 c m$ respectively and resistivity $ρ = 3.5 \times 1 0^{- 5} Ω m$ . The resistance of the configuration for the length of $5 c m$ cylinder is $\times 1 0^{- 3} Ω$ .

$7.42$

$10.56$

$14.38$

$16.48$

Q. A resistor is constructed as a hollow cylinder with inner and outer radii ra​=0.5cm , rb​=1.0cm respectively and resistivity ρ=3.5×10−5Ωm . The resistance of the configuration for the length of 5cm cylinder is ×10−3Ω .

7.42

10.56

14.38

16.48

Given. l=5cm=5×10−2m ρ=3.5×10−5Ωm A=π(1×10−4−0.25×10−4) =0.75π×10−4m2 =7.5π×10−5m2 ∴R=Aρl​=7.5π×10−53.5×10−5×5×10−2​ =7.42×10−3Ω

Q. A resistor is constructed as a hollow cylinder with inner and outer radii $r_{a} = 0.5 c m$ , $r_{b} = 1.0 c m$ respectively and resistivity $ρ = 3.5 \times 1 0^{- 5} Ω m$ . The resistance of the configuration for the length of $5 c m$ cylinder is $\times 1 0^{- 3} Ω$ .

$7.42$

$10.56$

$14.38$

$16.48$