Diameter of a wire with length, resistance and resistivity

In summary, the conversation is about the heated front windscreen of a car and the calculations needed to determine the current and resistance of the heater. The heater consists of resistance wires embedded in the glass and is powered by a car battery with negligible internal resistance. The current required to deliver a power of 180W is calculated to be 15A and the resistance of the heater is approximately 1 ohm. In addition, the heater consists of 200 wires connected in parallel and the equation for resistance is given as resistivity times length over cross-section area. The conversation ends with a request for the equation needed to calculate the diameter of the wires.
  • #1
Elka
2
0

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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  • #2
Welcome to PF!

Hi Elka! Welcome to PF! :smile:

Resistance = resistivity times length over cross-section area. :wink:​
 
  • #3
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
 

1. What is the relationship between wire diameter and resistance?

The resistance of a wire is inversely proportional to its diameter. This means that as the diameter of a wire increases, its resistance decreases. This relationship is known as the "skin effect."

2. How does wire length affect resistance?

The resistance of a wire is directly proportional to its length. This means that as the length of a wire increases, its resistance also increases. This is because a longer wire has more material for the current to travel through, resulting in a higher resistance.

3. What is resistivity and how does it relate to wire diameter?

Resistivity is a measure of a material's resistance to electrical current. It is affected by factors such as temperature and material type. The resistivity of a material also determines the wire's diameter, as higher resistivity materials require a larger diameter to achieve the same level of conductivity.

4. How can wire diameter, length, resistance, and resistivity be calculated?

Wire diameter can be measured directly using a micrometer or calculated using the wire's gauge number. Wire length can also be measured directly or calculated using the wire's spool size. Resistance can be measured using an ohmmeter or calculated using Ohm's law (R = V/I). Resistivity can be found in tables or by using the formula p = RA/l, where p is resistivity, R is resistance, A is cross-sectional area, and l is length.

5. How does temperature affect the diameter of a wire?

As temperature increases, the diameter of a wire can also increase due to thermal expansion. This can lead to an increase in resistance, which is why some materials are used for their low temperature coefficient of resistance (TCR) to reduce this effect.

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