A silver wire and a platinum wire of the same length have the same resistance. What is the ratio of the diameter of the silver wire to that of the platinum wire.
p1^L1/D1^2 = p2*L2/D2^2 since resistances are equal.
(The p's are the resistivities, which you need to look up). Since L1 = L2,
D1/D2 = sqrt(p2/p1)
subscript "1" denotes silver and subscript "2" denotes platinum.
To find the ratio of the diameter of the silver wire to the platinum wire, we need to consider the resistance of each wire.
The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area.
Let's assume the length of both the silver and platinum wires is the same.
We can write the equation for the resistance of a wire as:
R = (ρ * L) / A
Where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
Since the resistance of both wires is the same, we can set up the equation as follows:
(ρ1 * L) / A1 = (ρ2 * L) / A2
Here, ρ1 and ρ2 are the resistivities of silver and platinum wires, respectively. A1 and A2 are the cross-sectional areas of the silver and platinum wires, respectively.
Since we are asked to find the ratio of the diameters of the two wires, we need the relationship between the cross-sectional areas of the wires:
A1 = π * (d1/2)^2 and A2 = π * (d2/2)^2
Where d1 and d2 are the diameters of the silver and platinum wires, respectively.
Now, we can substitute these values into the equation:
(ρ1 * L) / (π * (d1/2)^2) = (ρ2 * L) / (π * (d2/2)^2)
We can simplify the equation by canceling out the common terms, such as L and π:
(ρ1 * (d2/2)^2) = (ρ2 * (d1/2)^2)
To find the ratio of the diameter of the silver wire to the platinum wire, we need to isolate the diameters.
Let's divide both sides of the equation by (ρ1 * (d2/2)^2):
d2^2 / d1^2 = ρ2 / ρ1
Taking the square root of both sides gives us:
d2 / d1 = √(ρ2 / ρ1)
Now we have the ratio of the diameters:
d2 / d1
To calculate this ratio, you would need to look up the resistivity values (ρ) for silver and platinum, and then substitute those values into the equation. Once you have the resistivity values, you can calculate the ratio using the square root of ρ2 divided by ρ1.