A copper wire has a diameter 0.5mm and restivity 1.6×10^-8ohms
(A) what is length of this wire to make resistance 12ohms
(B) how much will be the resistance of another copper wire of same length but half the diameter
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The area of cross section of copper wire = 22/7 * (0.5/2)^2 / 1000 m^2
= 0.1964 / 1000 = 0.0001964 m^2
Resistivity = 1.6 * 10 ^ -8
L = ?
Resistance = 12 ohm
R = Rho * L/A
12 = 1.6 * 10^ -8 * L / 0.0001964
12 * 0.0001964 / 1.6 * 10 ^ -8 = L
L = 1473 m
The resistance of the same length of wire but of half diameter will be half of the previous one which is 6 ohm.
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