A 230-W heating coil designed to operate from 110 V is made of Nichrome wire 0.7

Question

A 230-W heating coil designed to operate from 110 V is made of Nichrome wire 0.770 mm in diameter. (Assume

A 230-W heating coil designed to operate from 110 V is made of Nichrome wire 0.770 mm in diameter. (Assume ? = 1.50 X 10^-4 for Nichrome. a) Assuming the resistivity of the Nichrome remains constant at its 20.0°C value, find the length of wire used. m 16.32 (b) Now consider the variation of resistivity with temperature. What power is delivered to the coil of part (a) when it is warmed to 1 200°C? . W X 10^-6? · m, and ? = 4.000

Explanation / Answer

R = V^2/P = 110*110/230 = 52.61 ohm

a. Now: R =rho*L/A

=> L = R*A/rho = 52.61*3.14*.77*.77*10-6/4*1.5*10-6 = 16.32 m

b. L = L0 (1+ alpha* delta T) = 16.32*(1+ 4*10-4*1200) = 24.1536 m

therefore, R = rho*L/A = 1.5*10-6*24.1536*4/ 3.14*.77*.77*10-6 = 77.84 ohm

therefore power = V*V/R = 110*110/77.84 = 155.45 W

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