the resistance of a certain length wire having diameter 5mm is 10 omega if the diameter is change to 10 mm the new resistance in omega is
resistance is inversely proportional to area.
R=10Megaohm*(5/10)^2
To find the new resistance when the diameter of the wire changes, we need to use the formula for resistance of a wire:
R = (ρ * L) / A
where:
- R is the resistance,
- ρ (rho) is the resistivity of the material (a constant),
- L is the length of the wire, and
- A is the cross-sectional area of the wire.
Since we are given the resistance and length of the wire, we need to find the cross-sectional area before and after the diameter change in order to calculate the new resistance.
The cross-sectional area of a wire is given by the formula:
A = π * (r^2)
where:
- π (pi) is a mathematical constant approximately equal to 3.14159,
- r is the radius of the wire.
First, let's calculate the initial cross-sectional area:
Given diameter = 5 mm
Radius (initial) = diameter / 2 = 5 mm / 2 = 2.5 mm = 0.0025 m
Using the formula for the cross-sectional area:
A (initial) = π * (0.0025^2) = 3.14159 * (0.0025^2) = 1.9635e-05 m^2
Now, let's calculate the new cross-sectional area:
New diameter = 10 mm
New radius = new diameter / 2 = 10 mm / 2 = 5 mm = 0.005 m
Using the formula for the cross-sectional area:
A (new) = π * (0.005^2) = 3.14159 * (0.005^2) = 7.854e-05 m^2
Finally, let's find the new resistance using the given resistance and the new cross-sectional area:
Given resistance = 10 Ω
New resistance = (ρ * L) / A (new)
Since the resistivity ρ and the length L remain constant, we can write:
New resistance = (ρ * L) / A (new) = (ρ * L) / (7.854e-05)
It's important to note that we don't have enough information about the material's resistivity or the length of the wire, so we cannot calculate the exact new resistance without that information.