23. A wire of length 1 m and uniform diameter has a resistance of 1.05 ohm. What length of the wire of the same material, but having half the diameter, would be needed to make a 5ohm coil?
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Answer:
=> R = pL/A
=> where,
R= resistance
p = resistivity
L = length
A = area
=> resistance of the wire is inversely propotional to the the area.
∴ 1.05 = p * 1 / A... (1)
=> when taking the wire of the same material, but having half the diameter then it have 4 times the resistance/unit length and 1/4 the area
∴ 5 = p* L /(A/4) ... (2)
=> By dividing equation (2) by equation (1), we obtain,
5/1.05 = 4L
4.76 = 4L
L = 4.76/4
L = 1.19 m
Thus, the length of the wire of the same material, but having half the diameter, would be 1.19 m.
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