A cylindrical resistor of length \(l\) is made from a metal of mass \(m\). It has a resistance \(R\).

Two resistors, each of length \(2l\) and mass \(\frac{m}{2}\), are then created from the same volume of the metal.

What is the resistance of the two resistors when connected in parallel?

A.     \(R\)

B.     \(2R\)

C.     \(4R\)

D.     \(8R\)

C

Think proportionality.

There were a few G2 comments suggesting that this question was too complex and took too much time, but this is only the case if candidates reach for equations before considering proportionality.

A simple sketch will show that if the new resistors are placed side by side (ie in parallel) then the new length is twice the previous length (leading to a doubling of the resistance) and half its cross-sectional area (leading to a further doubling of the resistance). So the correct response is C.