Question

The resistance of wire in a heater at room temperature is 65 ohm. when the heater is connected to a 220V supply the current settles after a few seconds to 2.8A. What is the steady temperature of the wire? (temperature coefficient of resistance ,alpha=1.70×10^4°C^-)

Answer 1

Answer:867°C

Explanation:

at room temperature 27°C , the resistance of the heating element is

[ according to Ohm's law, V = IR , so , R = V/I ]

at the steady temperature t°C , the resistance ,

=230/2.8 =

now, use the relation,

here, R=R_t = 82.143

now, 82.143 = 71.875 [1 + 1.7 × 10^-4(t - 27)]

=> 82.143 - 71.875 = 71.875 × 1.7 × 10^-4(t - 27)

=> 0.084 × 10^4 = t - 27

=> 840 + 27 = t

=> t = 867°C

hence, temperature = 867°C