Confused by a resistance question?! Please help me!

  • 0 votes

Here is the question:

The heating element for an electric fire is made from a wire of resistance R. It is replaced with a wire of the same material which has the same length but is twice the diameter. The resistance of this second wire is

Choice of answers: A) 1/4R,    B) 1/2R,    C) 4R,    D) 2R

I know that the answer is A) 1/4R, but can someone explain why???

Thanks ;)

Posted Fri 18th January, 2013 @ 19:54 by Tilly - Team GR
Edited by Tilly - Team GR on Fri 18th January, 2013 @ 19:54

3 Answers

  • 1 vote

I think it's something to do with area for a circle pi x radius squared, so if you increase the diameter by a factor of 2, then you're increasing the radius by a factor of 4 so the resistance decreases by the same factor of the radius. 

It has to be a lower resistance anyway because if it's made bigger, then there's more room for electrons to travel through which is easier.

Hope this helps, it is really confusing...

Answered Fri 18th January, 2013 @ 19:57 by Joanne
  • 0 votes

Thank you!!! I just tried a practice Q and I thought it was 1/2, but now I get why it's a 1/4.

:)

Answered Fri 18th January, 2013 @ 20:13 by Tilly - Team GR
  • 0 votes

Oh okay :)

Answered Fri 18th January, 2013 @ 22:22 by Joanne