Question

A metallic cylindrical wire 'A' has length 10 cm and radius 3 mm. Another hollow cylindrical wire 'B' of the same metal has length 10 cm, inner radius 3 mm and outer radius 4 mm. The ratio of the resistance of the wires A to B is: 

• A. \(\frac{7}{9}\)
• B. \(\frac{9}{7}\)
• C. \(\frac{9}{16}\)
• D. \(\frac{16}{9}\)
• E. \(\frac{3}{4}\)

Answer 1

The Correct Option is A

The correct option is (A): \(\frac{7}{9}\)
\(B=  \frac{ρL}{A}​\)
where:

• ρ is the resistivity of the material,
• L is the length of the wire,
• A is the cross-sectional area of the wire.
  Given:
• Wire A is a solid cylinder with length L=10 cm and radius r=3 mm.
• Wire B is a hollow cylinder with length L=10 cm, inner radius ri​=3 mm, and outer radius r_o​=4 mm.
  By calculating the cross-sectional  and resistances area using the resistance formula \(R=\frac{ρL}{A}\)
  ​Finally, we find the ratio \(\frac{R_A}{R_B}\)​​:
  \(\frac{R_A}{R_B}\)=\(\frac{7}{9}\)