A copper wire has diameter 0.5 mm and resistivity of 1.6 × 10–8 Ω m. What will be the length of this wire to make its resistance 10 Ω? How much does the resistance change if the diameter is doubled?
Resistance (R) of a copper wire of length l and cross-section A is given by the expression,
Where,
Resistivity of copper, p = 1.6 x 10-8 Ω m
Area of cross-section of the wire,
Diameter = 0.5 mm = 0.0005 m
Resistance, R = 10 Ω
Hence, length of the wire,
If the diameter of the wire is doubled, new diameter = 2x0.5 = 1 mm = 0.001 m
Therefore, resistance R'
Therefore, the length of the wire is 122.7 m and the new resistance is 2.5 Ω
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(a) Why is the tungsten used almost exclusively for filament of electric lamps?
(b) Why are the conductors of electric heating devices, such as bread-toasters and electric irons, made of an alloy rather than a pure metal?
(c) Why is the series arrangement not used for domestic circuits?
(d) How does the resistance of a wire vary with its area of cross-section?
(e) Why are copper and aluminium wires usually employed for electricity transmission?
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