The specific resistance of nichrome is 100 micro-ohm-cm. Calculate the length of wire required to make a coil of 10 ohm? The diameter of wire used should be 0.4 mm.
Question
The specific resistance of nichrome is 100 micro-ohm-cm. Calculate the length of wire required to make a coil of 10 ohm? The diameter of wire used should be 0.4 mm.
Solution
To solve this problem, we need to use the formula for resistance:
R = ρ * (L/A)
where:
- R is the resistance (10 ohms in this case)
- ρ is the resistivity or specific resistance (100 micro-ohm-cm)
- L is the length of the wire (which we are trying to find)
- A is the cross-sectional area of the wire
First, we need to convert the diameter of the wire to cm (from mm) because the resistivity is given in micro-ohm-cm.
Diameter = 0.4 mm = 0.04 cm
The cross-sectional area (A) of the wire can be calculated using the formula for the area of a circle (since the wire is cylindrical):
A = π * (d/2)^2
Substituting the diameter into the formula gives:
A = π * (0.04/2)^2 = 0.001256 cm^2
Now we can substitute R, ρ, and A into the resistance formula and solve for L:
10 = 100 * 10^-6 * (L/0.001256)
Solving for L gives:
L = 10 / (100 * 10^-6 * 1/0.001256) = 125.6 cm
So, the length of the wire required to make a coil of 10 ohms is approximately 125.6 cm.
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