Wire resistor a has twice the length and twice the cross sectional area of wire resistor b. which of the following accurately compares the resistances of wire resistors a and b? a) wire a has twice the resistance of wire b. b) wire a has half the resistance of wire b. c) wire a has the same resistance as wire b. d) none of the above

Option (c) is the correct answer.

Explanation:

It is known that the relation between resistance, length and cross-sectional area is as follows.

          R =

Let the resistance of resistor A is denoted by R and the resistance of resistor B is denoted by R'.

Hence, for resistor A the expression for resistance according to the given data is as follows.

                 R =

On cancelling the common terms we get the expression as follows.

             R =

Now, the resistance for resistor B is as follows.

           R' =

Thus, we can conclude that the statement, Wire A has the same resistance as wire B, accurately compares the resistances of wire resistors A and B.  

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