Question

A tungsten wire has a radius of 0.081 mm and is heated from 20.0 to 1315 °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 2.0 A is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.

Answer 1

Given, Radius (ov) = 0.081 mm 20.091 xjö? m. Area(A) = 78² T (0.081 x103) 2 22.051 xjö? m 2 T2 = 1315°C &T=Tr-Ti = 1295°C Ti= 20 c a = 4:5 x 10 18/"c V-110 volt I: 2A Now using oum's law. Rez 110 = 552 at 1315°c at 2006 Resistance (R2 R2 = R(+XOT) 55= R1 (149.5 xióx 1295) Ri= 8085 2=800562 As we know, Resistivity of tungston wire Job xoorm at 20°c so using Equohen Ri= Il 4 8:054 8962: 5.6 xo'r? 2.061x17 so, l=q.gf m=2096m So length of wire (P) = 27m = 2.96m. CS Scanner with CamScanner

Given, Radius (%) = 0.081 mm -0.081 xidmi Area (A) = 782 T 10.081 +18)2 z 2,061 T, zo'c T2 = 1315c 8 XIO h, L &T= Tz-Ti = 1295°c x = 45 x 10 xio/c V = 110volt I = 2 Now using oum's low. v R2= 110 = 55 R at 1315°C I 2 -3 at 20°c Resistance (R.2 R2 = R(+4OT) 55= Ri (14 9.5 x16 x 1295) R1 = 9.4382 As we know, Resistivity of tungston wire gib xiorm at 20°C so using Equotson Ri= Il A s:6x10 l 9.438 8 2.061 x 10 l = 3.47 m so , So length of wire (1) = 3.47 m CS Scanned with CamScanner
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Given, Radius (%) = 0.081 mm -0.081 xidmi Area (A) = 782 T 10.081 +18)2 z 2,061 T, zo'c T2 = 1315c 8 XIO h, L &T= Tz-Ti = 1295°c x = 45 x 10 xio/c V = 110volt I = 2 Now using oum's low. v R2= 110 = 55 R at 1315°C I 2 -3 at 20°c Resistance (R.2 R2 = R(+4OT) 55= Ri (14 9.5 x16 x 1295) R1 = 9.4382 As we know, Resistivity of tungston wire gib xiorm at 20°C so using Equotson Ri= Il A s:6x10 l 9.438 8 2.061 x 10 l = 3.47 m so , So length of wire (1) = 3.47 m CS Scanned with CamScanner