Q. 76

Expert-verified
Found in: Page 765

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# 76. A thin metal cylinder of length and radius is coaxial with a thin metal cylinder of length and a larger radius . The space between the two coaxial cylinders is filled with a material that has resistivity . The two cylinders are connected to the terminals of a battery with potential difference , causing current to flow radially from the inner cylinder to the outer cylinder. Find an expression for the resistance of this device.

An expression for the resistance of this device is .

See the step by step solution

## Step 1: Given information

The two cylinders are connected to the terminals of a battery with potential difference , causing current to flow radially from the inner cylinder to the outer cylinder.

## Step 2: Explanation

The metal cylinders are light and have an enormous cover area, and will ignore their resistance and only regard the inner material's resistance. To uncover the resistance, split the space between the cylinder into little shots of thickness . The differential resistance of one of these shells will be similar to

The point that is the surface area of this cylindrical shell that recreates the cross-section's function via which the current flows. Now the total resistance is only the integral of where integrate from to of these shells:

## Step 3: Graphical Representation

An expression for the resistance of this device is .