Diameter of a wire with length, resistance and resistivity

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SUMMARY

The discussion centers on calculating the diameter of resistance wires used in a car's heated windscreen. The heater requires a power output of 180W, supplied by a 12V battery, resulting in a current of 15A and a resistance of approximately 1 ohm. The wires, totaling 200 in number, each have a length of 0.70m and a resistance of 160 ohms, with a resistivity of 6.0x10^-7 ohmic meters. The key equation for determining the diameter of the wire is based on the relationship between resistance, resistivity, length, and cross-sectional area.

PREREQUISITES
  • Understanding of electrical power calculations (P = IV)
  • Knowledge of Ohm's Law (V = IR)
  • Familiarity with the formula for resistance (R = ρL/A)
  • Basic concepts of resistivity and its units
NEXT STEPS
  • Research the formula for calculating the cross-sectional area of a wire (A = π(d/2)²)
  • Learn about the implications of wire resistance in parallel circuits
  • Explore the effects of resistivity on wire performance in different materials
  • Study the relationship between wire diameter and electrical resistance
USEFUL FOR

Students studying electrical engineering, physics enthusiasts, and anyone involved in automotive design or electrical circuit analysis will benefit from this discussion.

Elka
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Homework Statement


This question is about the heated front windscreen of a car
The heater consists of resistance wires which are embedded in the glass

A) The power of the heater needs to be 180W for a satisfactory demisting
A car battery of Negligable internal resistance supplies 12V to operate on the heated screen

Calculate the current required to deliver a power of 180W
180/12=15A

Show that the resistance of the heater when operating is about 1ohm
12/15=0.8 ohms, rounded up=1ohm

B) the heater consists of 200 wires inside the glass
These wires are connected in parallel to the 12V supply

Each of the 200 wires has a length of 0.70m and a resistance R(subscript)p of 160 ohms
The material of the wire has resistivity p=6.0x10^-7ohmic metres

Calculate the DIAMETER of the wire

please people, I don't want the answer, can someone just help me out and give me the equation I need to use? I'm terrible at remembering equations I really need the equation, thanks x
 
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Welcome to PF!

Hi Elka! Welcome to PF! :smile:

Resistance = resistivity times length over cross-section area. :wink:​
 
Thank you Tiny Tim! Thats great! You've helped me pick up 4 marks definitely and maybe 5! (past papers homeworks) Thank you so much, you're a lifesaver :D
 

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