the electrical resistance of a wire varies inversely as the square of the radius.if the resistance is 0.24ohms the radius is 0.05. Find the resistance when the radius is 0.04. Solve using variation

Question

An abstract representation of the concept of electrical resistance and wire radius. The main elements to include are two conductive wires, one with a larger radius and another one with a smaller radius. Use a variety of colors to differentiate between the wires. Include symbolic representations of resistance and variation, such as a resistor symbol, and have different color radii around the wires to indicate the change in their sizes. Please ensure the image does not include any text.

the electrical resistance of a wire varies inversely as the square of the radius.if the resistance is 0.24ohms the radius is 0.05. Find the resistance when the radius is 0.04. Solve using variation

Answer 1

R = k/r^2

when R = .24, r = .05
.24 = k/.0025
k = .006

when r = .04
R = .006(1/.0016) = .375

Answer 2

Why did the wire go on a diet? Because it wanted to resist less!

To solve this variation problem, we can set up a proportion. Let's call the resistance R and the radius r.

According to the problem, the electrical resistance (R) varies inversely as the square of the radius (r). In mathematical form, this can be written as:

R = k/r^2

Where k is the constant of variation.

We are given the resistance and radius of one situation, R1 = 0.24 ohms and r1 = 0.05. Let's substitute these values into the equation to find the value of k:

0.24 = k/(0.05)^2
0.24 = k/0.0025
k = 0.24 x 0.0025
k = 0.0006

Now that we have the value of k, we can use it to find the resistance (R2) when the radius (r2) is 0.04:

R2 = k/r2^2
R2 = 0.0006/(0.04)^2
R2 = 0.0006/0.0016
R2 ≈ 0.375 ohms

So, when the radius is 0.04, the resistance is approximately 0.375 ohms.

Answer 3

To solve this variation problem, we can start by defining the inverse square relationship between resistance and radius as follows:

Resistance ∝ 1/ (radius^2)

Let's assign variables to the resistance (R) and radius (r):

R ∝ 1/ (r^2)

Now, let's substitute the given values into the equation:

0.24 Ω ∝ 1/ (0.05^2)

To find the constant of variation, we need to solve for it. We can cross-multiply to get:

0.24 Ω = 1/ (0.05^2)

0.24 Ω = 1 / 0.0025

0.24 Ω = 400 Ω

Now that we have the constant of variation, we can use it to find the resistance when the radius is 0.04. Let's substitute the new radius into the equation:

R ∝ 1/ (0.04^2)

R ∝ 1/ 0.0016

R ∝ 625 Ω

Therefore, when the radius is 0.04, the resistance is 625 ohms.

Answer 4

To solve this problem using variation, we need to understand the relationship between resistance and radius. According to the given information, the electrical resistance of a wire varies inversely as the square of the radius. This can be represented mathematically as:

R = k/r²

where R is the electrical resistance, r is the radius, and k is the constant of variation.

We have been given that when the resistance is 0.24 ohms, the radius is 0.05. Let's use this information to find the value of the constant of variation (k).

0.24 = k / (0.05)²

Simplifying the equation:

0.24 = k / 0.0025

To find the value of k, we can multiply both sides of the equation by 0.0025:

k = 0.24 * 0.0025

k = 0.0006

Now that we have the value of the constant of variation (k), we can use it to find the resistance when the radius is 0.04:

R = k / (0.04)²

Substituting the value of k:

R = 0.0006 / 0.0016

This simplifies to:

R = 0.375 ohms

So, when the radius is 0.04, the resistance is 0.375 ohms.