The heating element for an electric fire is made from a wire of resistanceR. 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???
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.