How Do You Calculate the Radius of a Wire Using Electrical Resistance Formulas?

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SUMMARY

The discussion focuses on calculating the radius of a wire using electrical resistance formulas, specifically the formula R = ρL/A. A participant struggled to derive the correct radius from given multiple-choice answers (10^-3 m, 10^-4 m, or 10^-5 m) due to incorrect unit conversions and calculations. The correct approach involves determining the resistance using Ohm's Law (V = IR) and then applying the resistance formula to find the wire's cross-sectional area and radius. Key calculations include using the charge of an electron (1.6 x 10^-19 C) and ensuring accurate unit conversions throughout the process.

PREREQUISITES
  • Understanding of Ohm's Law (V = IR)
  • Familiarity with the resistance formula R = ρL/A
  • Knowledge of unit conversions in electrical calculations
  • Basic understanding of electrical charge (1 electron = 1.6 x 10^-19 C)
NEXT STEPS
  • Study the derivation of the resistance formula R = ρL/A in detail
  • Learn about unit conversion techniques in electrical engineering
  • Explore practical applications of Ohm's Law in circuit analysis
  • Investigate the relationship between current, voltage, and resistance in various materials
USEFUL FOR

Students in electrical engineering, educators teaching circuit theory, and professionals involved in wire design and electrical resistance calculations will benefit from this discussion.

elenour
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Homework Statement
A wire of resistivity 3.14x10^-7 ohm m. and of length 200m. If this wire allows a flow of 2x10^19 electrons each second when its connected to a power supply of 64V, find the radius of the wire.
Relevant Equations
pi=3.14
e=1.6x10^-19 c
i really have tried all the formulas out there and can't seem to get a solid answer
 
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Mr Ohm Is a good friend.
 
Show us what you tried and tell us why you think it's wrong.
 
Last edited:
vela said:
Show us what you tried and tell us why you think it's wrong.
I know the answers i get are wrong because its a multiple choice question and the answers are 10^-3 m, 10^-4 m or 10^-5 m and i haven't been getting close to any 10's.
I just want to know how to solve the problem :H
 
elenour said:
I know the answers i get are wrong because its a multiple choice question and the answers are 10^-3 m, 10^-4 m or 10^-5 m and i haven't been getting close to any 10's.
I just want to know how to solve the problem :H
Per forum rules, you must post at least one of your attempts.
 
I think you are making some mistakes in the unit conversions, if we assume your approach to be correct.
1 electron contains 1.6*10^-19 C charge. So first multiply number of electron into charge, which gives us 3.2 A current. Use the formula V = IR, and calculate R. R comes out to be 20 ohms. Now calculate using the formula for resistance R= ρL/A, Find the area and then the radius of the wire according.
 

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