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:
2/3
1/3
3/3
4/2
3/2

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

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.

To find the power delivered to wire A compared to the power delivered to wire B, we need to consider the electrical properties and dimensions of both wires.

Let's start with some given information:
- Wire A is three times as long as wire B.
- The radius of wire A is twice that of wire B.
- The resistivity of wire A is double that of wire B.
- Both wires are connected to the same potential difference.

To find the power delivered to each wire, we need to use the formula:

Power = (Current)^2 * Resistance

First, let's compare the resistances of the two wires. The resistance of a wire is given by the formula:

Resistance = (Resistivity * Length) / Cross-sectional area

Given that wire A has double the resistivity of wire B, we can say that the resistance of wire A will be double that of wire B, assuming the lengths and cross-sectional areas are the same.

Next, let's consider the dimensions of the two wires. Wire A is three times longer than wire B and has a radius that is twice that of wire B. This means that wire A has a larger cross-sectional area than wire B.

The cross-sectional area of a sphere is given by the formula:

Area = π * (radius)^2

Comparing the cross-sectional areas of the two wires, we can see that the area of wire A will be four times that of wire B, given that the radius of wire A is double that of wire B.

Now, let's consider the current flowing through each wire. Since both wires are connected to the same potential difference, the current flowing through each wire will be the same.

Given that the power is equal to (current)^2 * resistance, and the resistance of wire A is double that of wire B, and the current is the same, we can conclude that the power delivered to wire A will be four times that of wire B.

Therefore, the correct answer is 4/2, as wire A receives four times the power delivered to wire B.