Two spherical conducting wires A and B are connected to the same potential difference. Wire A is three times as long as wire B, with a radius double that of wire B and resistivity doubles that of wire B. What is the power delivered to wire A to the power delivered to wire B?

Question

The MCQ answers are:
2/3
1/3
3/3
4/2
3/2

Answer 1

I assume your wires are round, not spherical. That is, they have a circular cross-section.

If A has power P, and cross-section area a, length m and resistivity r, then its resistance

R = rm/a

P = E^2/R
E^2/(rm/a) = aE^2/rm

Conductor B has power
(2a)E^2/(2r*3m) = 4/6 aE^2/rm = 2/3 P

Answer 2

oops
double radius is 4 x area, so

B has 4/3 the power.

I assume the answer choice 4/2 is a typo, since usually fractions are reduced.