How does the resistance of a copper wire change when both the length and diameter of the wire are double?

Question

How does the resistance of a copper wire change when both the length and diameter of the wire are doubled?

(a)
It decreases by a factor of two.
(b)
It increases by a factor of two.
(c)
It increases by a factor of four.
(d)
It decreases by a factor of four.
(e)
It does not change.

Answer 1

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the resistance of a wire is given by

R=rho L/A where rho is a characteristic of the material, L is the length and A is the cross sectional area

if the diameter is doubled then the cross sectional area is quadrupled; the resistance varies as 2L/4A or 1/2 the original resistance; in this case, the resistance decreases by a factor of 2, or Ans A is correct

Answer 2

Resistance = k x length / ( pi/4 ) d^2
Let Resistance is R ohms
(a)
It decreases by a factor of two. new Resistance 4/2 = 2 R

(b)
It increases by a factor of two. new resistance = 2/4 = 0.5 R

(c)
It increases by a factor of four.new resistance = 4/16 = 0.25 R

(d)
It decreases by a factor of four. new resistance = 16 /4 = 4 R

(e)
It does not change.new resistance = R