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?
The MCQ answers are:
Electricity help needed please - Steve, Friday, November 15, 2013 at 12:49pm
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
Electricity - correction - Steve, Friday, November 15, 2013 at 12:51pm
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.