a copper wire has a diameter of o.5mm and resistivity of 1.6*10power 6 ohm cm.calculate the length of wire which will be necessary to make 10 ohm coil
To calculate the length of wire needed to make a 10 ohm coil, we need to use the formula for the resistance of a wire:
R = (ρ * L) / A
Where:
R is the resistance of the wire,
ρ is the resistivity of the material (1.6 * 10^6 ohm cm for copper),
L is the length of the wire, and
A is the cross-sectional area of the wire.
First, let's convert the diameter of the wire to its radius:
Radius = diameter / 2 = 0.5 mm / 2 = 0.25 mm = 0.025 cm
Next, we need to calculate the cross-sectional area of the wire:
A = π * r^2
A = π * (0.025 cm)^2
Now, let's plug in the given values into our formula and solve for the length of the wire:
R = 10 ohm
ρ = 1.6 * 10^6 ohm cm
A = π * (0.025 cm)^2
10 ohm = (1.6 * 10^6 ohm cm * L) / (π * (0.025 cm)^2)
To isolate L, we can rearrange the formula:
L = (10 ohm * π * (0.025 cm)^2) / (1.6 * 10^6 ohm cm)
L ≈ 0.098 m
Therefore, approximately 0.098 meters (or 9.8 cm) of copper wire with a diameter of 0.5 mm and a resistivity of 1.6 * 10^6 ohm cm would be needed to make a 10 ohm coil.