Resistance

[jazz2112]

I have no clue how to start this question.

Question: The electrical resistance of 1 metre of a certain wire is directly proportional the square of the diameter of the wire. Wire with a diameter of 2mm has a resistance of 1.20 Ohms.

a) Write a formula for the electrical resistance of the 1m wire as a function of its diameter.

b) Determine the electrical resistance of a wire with a diameter of 5mm.

 

[MarkFL]

Let's let \(R\) be the resistance in ohms of the 1 m segment of wire, and \(D\) is the diameter of the wire in mm. From the statement:

"The electrical resistance of 1 metre of a certain wire is directly proportional [to] the square of the diameter of the wire. "

We may write:

[MATH]R=kD^2[/MATH] where \(0<k\) is the constant of proportionality.

We need to find \(k\), and we are given a known resistance for a segment of wire with a known diameter. Can you use this information to find \(k\)?

 

[Dr.Peterson]

Question: The electrical resistance of 1 metre of a certain wire is directly proportional the square of the diameter of the wire. Wire with a diameter of 2mm has a resistance of 1.20 Ohms.

a) Write a formula for the electrical resistance of the 1m wire as a function of its diameter.

b) Determine the electrical resistance of a wire with a diameter of 5mm.

Please check that you copied the problem correctly. What is said is not true! Resistance is inversely proportional to the square of the diameter. (Thinner wire has more resistance.)

Problems like this don't have to be true, but in my experience they try not to be too far off.

But if you copied it correctly, then MarkFL told you what to do.

 

[jazz2112]

Yes it’s copied correctly, that’s why I was so confused on how to attempt the question! Thankyou guys for explaining