Now put this into practice

Question

1
A certain wire has a length of 10 m and a resistance of 600.
Calculate the resistance of 20 m of the wire.
2 A certain wire has diameter of 0.20 mm and a resistance
of 602. Calculate the resistance of a wire of the same
material with a diameter of 0.40 mm.

Answer 1

1) To calculate the resistance of 20 m of the wire, we can use the formula for resistance:

Resistance = (ρ * Length) / Area

Since the length is given as 10 m and the resistance is given as 600, we can rearrange the formula to solve for ρ (the resistivity):

ρ = (Resistance * Area) / Length

First, let's find the resistivity of the wire:

ρ = (600 * π * r^2) / 10

Since the diameter is not given, we need to find the radius first. The formula to convert diameter to radius is:

Radius = Diameter / 2

If the length is given in mm, we need to convert it to meters first. Since there are 1000 mm in 1 meter, the conversion factor is 0.001:

Length = 10 * 0.001 = 0.01 m

Let's assume the wire is cylindrical. The formula to calculate the area of a cylinder is:

Area = π * r^2

Now we can use the formula to find the resistivity:

ρ = (600 * π * r^2) / 0.01

2) To calculate the resistance of a wire with a diameter of 0.40 mm, we can follow a similar process.

First, let's convert the diameter to radius:

Radius = 0.4 / 2 = 0.2 mm

Now we need to convert the radius to meters:

Radius = 0.2 * 0.001 = 0.0002 m

Next, we calculate the area of the wire:

Area = π * (0.0002)^2

Finally, we can use the same formula to calculate the resistance:

Resistance = (ρ * Length) / Area

Since we already know the resistivity (ρ) from the previous calculation, we can substitute the values and calculate the resistance of the wire with a diameter of 0.40 mm.