### Problem DescriptionA material with a resistivity of \( 340000 \, \Omega \cdot \text{m} \) is formed into a hollow cylindrical shell. The shell has the following dimensions:- **Length (L):** 3 cm- **Inner radius (\( r_a \)):** 0.53 cm- **Outer radius (\( r_b \)):** 1.27 cmWhen a potential difference is applied between the ends of the cylinder, a current is produced parallel to its length.### ObjectiveFind the resistance of the cylinder. Provide the answer in units of megaohms (MΩ).### Diagram ExplanationThe diagram shows a hollow cylindrical shell:- The length of the cylinder is labeled as \( L \).- The inner radius is marked as \( r_a \).- The outer radius is labeled as \( r_b \).### Solution Steps1. **Convert all dimensions to meters:** - Length: \( L = 3 \, \text{cm} = 0.03 \, \text{m} \) - Inner radius: \( r_a = 0.53 \, \text{cm} = 0.0053 \, \text{m} \) - Outer radius: \( r_b = 1.27 \, \text{cm} = 0.0127 \, \text{m} \)2. **Determine the formula for resistance.** Resistance \( R \) of a cylindrical shell is given by: \[ R = \frac{\rho \,L}{A_{\text{eff}}} \] Where: - \( \rho \) is the resistivity - \( L \) is the length of the cylinder - \( A_{\text{eff}} \) is the effective cross-sectional area3. **Calculate the effective cross-sectional area \( A_{\text{eff}} \).** For a hollow cylinder: \[ A_{\text{eff}} = \pi (r_b^2 - r_a^2) \] Substituting the values: \[ A_{\text{eff}} = \pi (0.0127^2 - 0.0053^2) \, \text{m}^2 \]4. **Compute \( A_{\text A resistor is constructed by forming a ma-

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terial of resistivity 340000 · m into a shape of a hollow cylindrical shell of length 3 cm and inner radius of 0.53 cm and outer ra- dius 1.27 cm. In use, a potential difference is applied between the ends of the cylinder, pro- ducing a current parallel to the length of the cylinder. - L rb ra Find the resistance of the cylinder. Answer in units of MN.

terial of resistivity 340000 · m into a shape of a hollow cylindrical shell of length 3 cm and inner radius of 0.53 cm and outer ra- dius 1.27 cm. In use, a potential difference is applied between the ends of the cylinder, pro- ducing a current parallel to the length of the cylinder. - L rb ra Find the resistance of the cylinder. Answer in units of MN.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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