Question

At what temperature will gold have a resistivity that is three times the resistivity of iron at room temperature? C°C

Answer 1

Solution : Resistivity and Temperature relation is given by 8(T) = %.[1 + a (T-TJ] where, To is Resistivity of material at room temperature 'a'is temperature coefficient of resistivity To is room temperature In this case, the resistivity of the gold is 3 times the resistivity of iron art room temperature. Therefore, 300 ron - So (1+a (T-To)] The resistivity of iron at room temperature (sofern's g. 71 x 108 ohmm. The resistivity of gold at room temperature (80) is 2.248 10-8 ohm m. Temperature coefficient of resistance (a)= 0.0034/6 The temperature at which the resistivity of gold becomes & times the resistivity of iron at room temperature is,

3 Voliron, So (gold) {1+ a (T-To)] 3 x 9.71 x 100 ohmm = 2.24x150 ohmm. [1+ 0.0034/6(T-209] 29.13 410-8 ohmm = 2.24x108 [1 + 0.0034T - 0.068] [0.932 + 0.0034T/= 29.13x10-8 2.24x10-8 0.0034 T = 13.00 – 0.932 T = 12.07 0.0034 T = 355 0.7 C Answer Hence, At 3550 .7 °C temperature will gold have a restivity that is three times the resistivity of iron at room temperature.