A heating element has a resistance of 100 `Omega` at room temperature. When it is connected to a supply of 220 V, a steady current of 2A passes in it and temperature is `500^(@)C` more than room temperature. What is the temperature coefficient of resistance of the heating element ?

Options

A. `5 xx 10^(-4) ""^(@)C^(-1)`
B. `2 xx 10^(-4)""^(@)C^(-1)`
C. `1 xx 10^(-4) ""^(@)C^(-1)`
D. `0.5 xx 10^(-4) ""^(@)C^(-1)`

Answer

B

Explanation

Steady current of 2A flows through the wire when 220V potential difference is applied. Temperature in this state is `500 ""^(@)C` higher than room temperature. Resistance in this state can be calculated as follows:
`R= (V)/(I) = (220)/(2) = 110 Omega`
Let `R_(0)` be the resistance at room temperature
`rArr R_(0) = 100 Omega`
`R= R_(0) (1 + alpha t)`
`110 = 100 (1 + alpha 500) rArr alpha = 2 xx 10^(-4) ""^(@)C^(-1)` Hence option (b) is correct.