What length of a copper wire of cross-section area 0.01 mm2 will be needed to prepare a resistance of 1 kΩ? Resistivity of copper = 1.7 × 10–8 Ω m.
0.6km
Given,
Resistance of the wire, R=1000Ω
Resistivity of copper, = 1.7 × 10–8 Ω m
Area of cross-section, A=0.01 mm2=0.01×10-6 m2
Formula used,
The expression for the resistance, R, of a wire is
Where ρ is the resistivity, A is the area of cross-section and ‘l’ is the length of the wire.
Or the length of the wire for given area and Area of a cross section is,
Solution,
Substituting the values in eqn.2, we get the required length as,
Hence the length of the copper wire for the given resistance is 0.6km.