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A copper wire has diameter 0.5mm and resistivity of 1.6*10(to the power -8) ohm m.what will be the length of this wire to make its resistance 10 ohm?how much does the resistance change if the diameter is doubled?

Asked by vaishakhautade25 10th June 2017, 2:52 PM
Answered by Expert
begin mathsize 12px style Resistance space of space straight a space wire space is straight R equals ρl over straight A equals fraction numerator ρl over denominator straight pi begin display style straight d squared over 4 end style end fraction equals fraction numerator 4 ρl over denominator πd squared end fraction straight l equals fraction numerator πd squared straight R over denominator 4 straight rho end fraction equals fraction numerator 3.14 cross times open parentheses 0.5 cross times 10 to the power of negative 3 end exponent close parentheses squared over denominator 4 cross times 1.6 cross times 10 to the power of negative 8 end exponent end fraction straight l equals 12.27 space straight m end style
From the expression of resistance, it is clear that it is inversely proportional to the square of diameter.
Hence, if the diameter is doubled, resistance becomes 0ne-fourth. In the above example the resistance
would become 10/4= 2.5 Ω
Answered by Expert 11th June 2017, 2:25 PM
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