Physics

Current Electricity

Properties of conductors

A conductor having resistivity is bent in the shape of a half

Question

Hard

Solving time: 4 mins

A conductor having resistivity $ρ$ is bent in the shape of a half cylinder as shown in the figure. The inner and outer radii of the cylinder are $a$ and $b$ respectively and the height of the cylinder is $h$ . A potential difference is applied across the two rectangular faces of the conductor. Calculate the resistance offered by the conductor.

Name: Video answer for A conductor having resistivity ρ is bent in the shape of a half cylinder as shown in the figure. The inner and outer radii of the cylinder are a and b respectively and the height of the cylinder is h. A potential difference is applied across the two rectangular faces of the conductor. Calculate the resistance offered by the conductor.
Uploaded: 2022-08-31T04:59:55.000Z
Duration: 7 min
Description: A conductor having resistivity ρ is bent in the shape of a half cylinder as shown in the figure. The inner and outer radii of the cylinder are a and b respectively and the height of the cylinder is h. A potential difference is applied across the two rectangular faces of the conductor. Calculate the resistance offered by the conductor.

Views: 5,775 students

Updated on: Aug 31, 2022

Book:

Problems in Physics II for IIT JEE (McGraw Hill)

Text solutionVerified

Consider a strip of width

d x

shown on the rectangular face in the figure Think of a half cylindrical conductor of radius

x

and infinitesimally small thickness

d x

. Length of this conductor

= π x

Cross sectional area of this conductor

= h d x

∴

Resistance of this thin cylindrical conductor

d R = \frac{ρ π x}{h d x}

The given conductor is made of countless number of such thin conductors, all connected in parallel.

∴

\frac{1}{R} R = \int \frac{1}{d R} = \frac{h}{ρ π} \int_{a}^{b} \frac{d x}{x} = \frac{h}{ρ π} ln (\frac{b}{a}) = \frac{ρ π}{h ln ( b / a )}

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Samuel Discussed

A conductor having resistivity

ρ

is bent in the shape of a half cylinder as shown in the figure. The inner and outer radii of the cylinder are

a

and

b

respectively and the height of the cylinder is

h

. A potential difference is applied across the two rectangular faces of the conductor. Calculate the resistance offered by the conductor.

13 mins ago

Discuss this question LIVE

13 mins ago

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Question Text	A conductor having resistivity $ρ$ is bent in the shape of a half cylinder as shown in the figure. The inner and outer radii of the cylinder are $a$ and $b$ respectively and the height of the cylinder is $h$ . A potential difference is applied across the two rectangular faces of the conductor. Calculate the resistance offered by the conductor.
Updated On	Aug 31, 2022
Topic	Current Electricity
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 1
Upvotes	194
Avg. Video Duration	7 min

Text solutionVerified

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Text solutionVerified

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