   Chapter 17, Problem 65AP

Chapter
Section
Textbook Problem

A resistor is constructed by forming a material of resistivity 3.5 × 105 Ω · m into the shape of a hollow cylinder of length 4.0 cm and inner and outer radii 0.50 cm and 1.2 cm, respectively. In use, a potential difference is applied between the ends of the cylinder, producing a current parallel to the length of the cylinder. Find the resistance of the cylinder.

To determine
The resistance of resistor in form of hollow cylinder.

Explanation

Given Info: The shape of resistor is a hollow cylinder with inner radius 0.50cm and outer radius 1.2cm . The length of cylinder is 4.0cm . The resistivity of the material of resistor is 3.5×105Ωm .

Explanation:

Formula to calculate the area of cross section is,

A=π(Router2rinner2)

• A is the area of cross section of hollow cylinder,
• Router is the outer radius,
• rinner is the inner radius,

Formula to calculate the resistance is,

R=ρLA

• R is the resistance of resistor,
• ρ is the resistivity of the material of resistor,
• L is the length of the resistor,

Use π(Router2rinner2) for A in the above equation to rewrite R.

R=ρLπ(Router2rinner2)

Substitute 3

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