# PHYSICS

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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 =0.00603 (C°)-1 and a resistivity of 5.00 x 10-7Ω m. For the second, the temperature coefficient is α2 = -0.000670 (C°) -1 and the resistivity is 6.20 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.

• PHYSICS - ,

(1/α)=R*(L/A), solve for A

α*R*L=A

1/α1 =1/0.00603 (C°)-1=5.00 x 10-7Ω m *(L/A)

Solving for A,

(0.00603 (C°))*(5.00 x 10-7Ω m) *(L1)=A

Solving for A,

1/α2 = 1/-0.000670 (C°) -1= 6.20 x 10-5Ω m *(L/A)

(0.000670 (C°) -)*(6.20 x 10-5Ω m)*(L2)=A

Set equations = to each other since both areas are the same.

α1*R1*L1=α2*R2*L2

(0.00603 (C°))*(5.00 x 10-7Ω m) *(L1)=(0.000670 (C°) -)*(6.20 x 10-5Ω m)*(L2)

L1/L2=α2*R2/α1*R1

[(L1)/(L2)]=[(0.000670 (C°) -)*(6.20 x 10-5Ω m)/(0.00603 (C°))*(5.00 x 10-7Ω m)]

Plug in your values and solve. Verify for yourself or wait for someone else to verify on this post.