Two wires have the same cross-sectional area and are joined end to end to form a single wire. The first wire has a temperature coefficient of resistivity of α1 =0.00480 (C°)-1 and a resistivity of 4.90 x 10-5Ω m. For the second, the temperature coefficient is α2 = -0.000600 (C°) -1 and the resistivity is 4.60 x 10-5Ω m, respectively. The total resistance of the composite wire is the sum of the resistances of the pieces. The total resistance of the composite does not change with temperature. What is the ratio of the length of the first section to the length of the second section? Ignore any changes in length due to thermal expansion.
resistanc=resitivity*length/Area * coeffThermal*deltaTemp
setting resistance the same
resisitive1*length1/area1*coeff1*dettaT1=resistivity1*length2/area2*cxoeff2*deltatT2
areas, deltatemps are same, so in my head..
length1/length2=coeff2/coeff1 * resisitive2/resisitivity1
check my thinking.
To solve this problem, we need to determine the ratio of the length of the first section to the length of the second section. We can set up an equation using the resistivity and temperature coefficient of resistivity.
Let's denote the lengths of the first and second sections as L1 and L2, respectively.
The resistance of a wire can be calculated using the formula: R = ρ * (L / A), where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area.
For the first section, the resistance is: R1 = ρ1 * (L1 / A).
For the second section, the resistance is: R2 = ρ2 * (L2 / A).
Since the total resistance of the composite wire does not change with temperature, we can set the two resistance equations equal to each other:
R1 + R2 = R2 + R1 (since R1 = R2)
ρ1 * (L1 / A) + ρ2 * (L2 / A) = ρ2 * (L2 / A) + ρ1 * (L1 / A)
Next, we can isolate the length ratios:
ρ1 * L1 + ρ2 * L2 = ρ2 * L2 + ρ1 * L1
ρ1 * L1 - ρ1 * L1 = ρ2 * L2 - ρ2 * L2
0 = 0
Since we found that 0 = 0, this implies that the length ratios do not affect the equation and can have any value. Therefore, the ratio of the length of the first section to the length of the second section can be any value and does not affect the total resistance of the composite wire.