Answered: Calculate the diameter of a 3.15 cm…

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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Question

Calculate the diameter of a 3.15 cm long tungsten filament in a lightbulb if its resistance is 0.341 Ω. (The resistivity of tungsten is 5.60×10^-8 Ωm.)

Expert Solution

Step 1

When current flows through a conductor then the opposition offered by the conductor to the current is termed as its resistance.

The formula to calculate the resistance is given by

$R = ρ \frac{l}{A}$

where $ρ$ is the resistivity of the filament, $A$ is the cross-sectional area of the filament and $l$ is the length of it.

Again the formula to calculate the cross sectional area is given by

$A = π r^{2}$ where $r$ is radius of the circuit.

Substitute this expression into the formula of the resistance and then rearrange to find an expression for the radius.

$R = ρ \frac{l}{π r^{2}} r^{2} = \frac{ρ l}{π R} r = \sqrt{\frac{ρ l}{π R}}$

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