A conducting wire is quadrupled in length and tripled in diameter. By what factor does its resistance change?

**Answer 1**

Quadrupling length will increase the resistance by 4 times: – (it’s like having 4 equal resistors in series)

Resistance is inversely proportional to the cross-sectional area (the larger the area the lower the resistance – the wider pipe analogy)

Because cross-sectional area = pi r^2 resistance must be inversely proportional to r^2

With a tripled diameter the radius is tripled also, so the resistance is reduced by a factor of 3^2

i.e. the resistance is 9 times less.

The overall effect is thus a change to 4 /9 ths of the original resistance value.

**Answer 2**

Resistance = ok x length / ( pi/4 ) d^2 enable Resistance is R ohms (a) It decreases via area of two. new Resistance 4/2 = 2 R (b) It will improve via area of two. new resistance = 2/4 = 0.5 R (c) It will improve via area of four.new resistance = 4/sixteen = 0.25 R (d) It decreases via area of four. new resistance = sixteen /4 = 4 R (e) It does not replace.new resistance = R

**Answer 3**

Decrease