A tungsten wire has a radius of 0.073 mm and is heated from 20.0 to 1500 °C. The temperature coefficient of resistivity is α = 4.5 10-3 (C°)−1. When 110 V is applied across the ends of the hot wire, a current of 1.6 A is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.
+33654 Resistance of wire at 1500°C is R = 110V/1.6A or R = 68.75 ohms
Electrical resistivity of tungsten at 20°C is rho20 = 5.5*10-8 ohm.m
Electrical resistivity of tungsten at 1500°C is rho1500 = rho20*(1 + alpha*deltaT)
rho1500 = 5.5*10-8*(1 + 4.5*10-3*(1500-20)) = 4.213*10-7 ohm.m
Length of tungsten wire at 1500°C L = rho1500/R or L = 4.213*10-7 ohm.m/68.75ohms ≈ 6*10-9 m
Hmm! Seems very short! Someone needs to check this.
+33654 Resistance of wire at 1500°C is R = 110V/1.6A or R = 68.75 ohms
Electrical resistivity of tungsten at 20°C is rho20 = 5.5*10-8 ohm.m
Electrical resistivity of tungsten at 1500°C is rho1500 = rho20*(1 + alpha*deltaT)
rho1500 = 5.5*10-8*(1 + 4.5*10-3*(1500-20)) = 4.213*10-7 ohm.m
Length of tungsten wire at 1500°C L = rho1500/R or L = 4.213*10-7 ohm.m/68.75ohms ≈ 6*10-9 m
Hmm! Seems very short! Someone needs to check this.
+1038 Solution:
R=110V1.6A=68.75 ohmsρ20=55.0∗10−9Ω⋅Mα=Temperature coefficient for tungsten=0.0045K−1(K−1≡C−1)ρ1500=(ρ20)∗[1+(αΔT)]ρ1500=(55.0∗10−9)∗(1+0.0045C−1)∗(1500−20)C=8.287125∗10−5M⋅ΩAc=(π∗r2)=π∗(0.073∗10−6)2=1.67415473∗10−8M2(Area cross-section)
R=ρ∗(L∗A)→Solve for length L. L=RA(ρ20∗[1+α∗ΔT])(68.75)∗(16.7415473∗10−9)(55.0∗10−9)∗(1+[0.0045∗1480])=2.73198 Meters
