Heating coil wire resistance and length of wire required

Click For Summary
SUMMARY

The discussion centers on calculating the resistance and length of Nichrome wire needed for a heating coil that draws 9.25 A at 120 V. The correct resistance calculation yields 12.973 Ohms using the formula R = V/I. For the length of wire, the proper formula R = ρl/A was clarified, leading to the conclusion that the length required is 255 meters, correcting earlier miscalculations related to unit conversions and area calculations.

PREREQUISITES
  • Understanding of Ohm's Law (R = V/I)
  • Knowledge of resistivity and its role in electrical resistance
  • Familiarity with the formula for cross-sectional area of a wire (A = πr²)
  • Basic unit conversion skills for electrical measurements
NEXT STEPS
  • Research the properties of Nichrome wire, including its resistivity
  • Learn about the impact of wire gauge on resistance and heating efficiency
  • Study advanced applications of Ohm's Law in electrical engineering
  • Explore practical examples of heating coil design and optimization
USEFUL FOR

Electrical engineers, physics students, and hobbyists involved in designing heating elements or studying electrical resistance in conductive materials.

servin247365
Messages
2
Reaction score
0

Homework Statement


A portion of Nichrome wire of radius 2.50 mm is to be used
in winding a heating coil. If the coil must draw a current of
9.25 A when a voltage of 120 V is applied across its ends,
find (a) the required resistance of the coil and (b) the
length of wire you must use to wind the coil.


Homework Equations


RI = V
R = I/oA



The Attempt at a Solution


(a) RI = V
R = V/I = 120V/9.25A = 12.973Ohms

(b)
R = l/oA
l = RoA = (12.973Ohms)(.000001ohms*m)(.0025m*3.14*2) = 2.036761e-7m

The answer to the second part of the equation is 255m and I can't figure out what I did wrong...

Thanks!
 
Physics news on Phys.org
Your units aren't working out well--equation for resistance seems odd.

Try R=ρl/A

ρ, resistivity in Ωm
l, length in m
A, cross-sectional area in m2.
 
Did you use the correct formula for area? Did you use a value for resistivity or conductivity for the symbol "o"?
 
Ah OK, that worked. I am not sure why the other formula from the book didn't show that but maybe I missed something... Thanks!
 

Similar threads

Long distance electrical transmission efficiency
  • · Replies 2 ·
Replies
2
Views
2K
Current and resistance of wire heating up water
  • · Replies 4 ·
Replies
4
Views
4K
Electric current and resistance question
  • · Replies 2 ·
Replies
2
Views
2K
How does the rise in temperature of fuse wire depend upon its radius?
  • · Replies 12 ·
Replies
12
Views
2K
Electrical energy converted to heat in coil
  • · Replies 15 ·
Replies
15
Views
3K
Measuring a Coil of Wire With Ohmmeter and Balance
  • · Replies 3 ·
Replies
3
Views
2K
Calculate number of turns for an electric heater
  • · Replies 3 ·
Replies
3
Views
2K
Finding New Resistance of a Length of Wire
  • · Replies 5 ·
Replies
5
Views
2K
Coils arrangement so the hotplate operates at 3 diff. powers
  • · Replies 25 ·
Replies
25
Views
3K
Ratio of the length of resistive wires in a square
  • · Replies 4 ·
Replies
4
Views
2K