Question

A tungsten wire has a radius of 0.090 mm and is heated from 20.0 to 1350 °C. The temperature coefficient of resistivity is α = 4.5 10-3 (C°)−1. When 240 V is applied across the ends of the hot wire, a current of 1.8 A is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.

____m

Answer 1

We know from the ohms law
V = IR
240 = 1.8*R
R = 133.33 ohm
Now we know that
R = pL/A
where p is the resistivity of tungsten = 5.6*10^-8 ohm/m
Area of the wire = Pi*r² = Pi*(0.09*10^-3)² = 2.545*10^-8 m²
Now from the resistance formula
L = RA /p = 133.33* 2.545*10^-8 / 5.6*10^-8 = 60.586 m
Now its length must be increased due to the temperature but we have not consider it so we will calculate original value of length .
L = L_o (1+(T₂ - T₁) )
L = L₀(1 + 4.5*10^-3 (1350- 20))
60.586 = L_o *(6.985)
L_o = 8.674 m
Hence this would be the original value of length of the wire.