Current and Electric Circuits :: Problem 12

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Problem 12: A 40Ω resistor is to be wound from platinum wire 0.1mm in diameter. How much wire is needed?

Solution:

Step: 1 Overview

See the overview of problem 2.

Given:

R=40Ω
ρ (for platinum)=1.1 x 10^-7Ω.m
d=0.01mm

Required:

L=?

Solution:

We know that,
r = d/2
r = (0.01mm)/2
r = 0.05mm = 5 x 10^-5m
Area=3.14r²
A=(3.14)(5 x 10^-5)²
A=(3.14)(25 x 10^-10)
A=7.85x10^-9

Also we know that:
R=ρL/A
RA=ρL
L=RA/ρ
L=(40)(7.85x10^-9)/(1.1x10^-7)
L=(3.14x10^-7)/(1.1x10^-7)
L=2.85m (Ans)