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 ratio power delivered to wire A to the power delivered to wire B? Power A/Power B

I am stuck on "sphereical" wires. I cant picture a spherical wire.

To find the ratio of power delivered to wire A to the power delivered to wire B (Power A/Power B), we need to consider the formulas for power in a circuit and the properties of the wires.

The power (P) in a circuit can be calculated using the formula:

P = (V^2) / R

Where:
P represents power in watts (W)
V represents the potential difference across the wire in volts (V)
R represents the resistance of the wire in ohms (Ω)

Let's break down the problem and find the values for each wire:

Wire A:
- Length (L) = 3 times the length of Wire B
- Radius (r) = double the radius of Wire B
- Resistivity (ρ) = double the resistivity of Wire B

Wire B:
- Length (L) = given
- Radius (r) = given
- Resistivity (ρ) = given

To simplify the problem, let's assume that Wire B has a length, radius, and resistivity of 1 unit. Therefore, Wire A will have a length of 3 units and a radius of 2 units.

Now, let's compare the properties of the wires:

Wire A:
- Length (L_A) = 3 units
- Radius (r_A) = 2 units
- Resistivity (ρ_A) = 2 * resistivity of Wire B

Wire B:
- Length (L_B) = 1 unit
- Radius (r_B) = 1 unit
- Resistivity (ρ_B) = given

From the formula for resistance (R):

R = (ρ * L) / (π * r^2)

We can see that resistance (R) is directly proportional to resistivity (ρ), inversely proportional to the length (L), and inversely proportional to the square of the radius (r). Therefore, we can write the resistance ratio for Wire A to Wire B as:

R_A / R_B = (ρ_A * L_A) / (π * r_A^2) / (ρ_B * L_B) / (π * r_B^2)

Simplifying the equation by substituting the given values:

R_A / R_B = (2 * ρ_B * 3) / (π * (2^2)) / (ρ_B * 1) / (π * (1^2))
R_A / R_B = 12 / 4 = 3

This shows that the resistance of Wire A is three times that of Wire B.

Now, let's consider the power ratio:

(P_A / P_B) = [(V^2) / R_A] / [(V^2) / R_B]

Substituting the equation for R_A / R_B:

(P_A / P_B) = [(V^2) / (3 * R_B)] / [(V^2) / R_B]

Simplifying the equation:

(P_A / P_B) = 1 / (1/3) = 3

Therefore, the ratio of the power delivered to wire A to the power delivered to wire B (Power A/Power B) is 3:1.