1. The problem statement, all variables and given/known data For some applications, it is important that the value of a resistance not change with temperature. For example, suppose you made a resistor from a carbon resistor and a Nichrome wire-wound resistor connected together so the total resistance RT is the sum of their separate resistances. What value should each of these resistors have (at 20 °C) so that the combination is temperature independent? Express your answer in terms of RT and the temperature coefficients of resistance of carbon αC and Nichrome αN (specified at 20 °C). Note that αC < 0 but αN > 0. Hints Given: The total resistance of the series combination is simply the sum of the separate resistances. Use this fact to write an expression for R(T), the resistance of the combination as a function of temperature T. How can you express the condition that R is independent of T at T = 20°C? (Hint: The function R(T) must have zero slope at T = 0). Remember that αC < 0; then check that your resistances RC and RN are positive. The answer requires two separate equations, one for Resistivity of Carbon and another Resistivity of Nichrome. 2. Relevant equations R = pl/A where p = resistivity coefficient and l is the length R(T) = R0(1+a(T-T0) a = alpha (temperature coefficient) 3. The attempt at a solution Using the equation R(T) = R0(1+a(T-T0) I tried to plug in the value for resistivity of Carbon (3-60)*10^-5 and same for the Nichrome but I'm not sure whether to add them into one equation or use separate equations?