Question

The resistance of transmission line is 126 ohm at 20 degree centigrade. determine the resistance of the line at minus 35 degree centigrade that TCR of a material of transmission line is 0.00426 per degree centigrade at 0 degree centigrade

Answer 1

$Given: The resistance of a conductor at 20∘C is 3.15Ω and at 100∘C is 3.75Ω. </p><p></p><p>To find the temperature co-efficient of resistance of the conductor.</p><p></p><p>Solution:</p><p></p><p>Here R20=3.15,R100=3.75</p><p></p><p>We know that Rt=R0(1+αt)</p><p></p><p>where R0= resistance at 0∘C</p><p></p><p>and Rt= resistance at t∘C</p><p></p><p>α= temperature coefficient of resistance</p><p></p><p>Now, </p><p></p><p>R20=3.15=R0(1+20α)....(i)</p><p></p><p>R100=3.75=R0(1+100α)....(ii)</p><p></p><p>Dividing (i) and (ii), we get</p><p></p><p>R0(1+100α)R0(1+20α)=3.753.15⟹3.75(1+20α)=3.15(1+100α)⟹3.75+75α=3.15+315α⟹240α=0.6⟹α=0.0025∘C−1</p><p></p><p>From equation(i) ,</p><p></p><p>R0=1+20α3.15⟹R0=1+20(0.0025)3.15⟹R0=1+0.053.15⟹R0=3Ω</p><p></p><p>is the temperature co-efficient of resistance of the conductor.$

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