The resistance of a wire at room temperature `30^(@)C` is found to be `10 Omega` . Now to increase the resistance by `10%` , the temperature of the wire must be [ The temperature coefficient of resistance of the material of the wire is `0.002` per `.^(@)C`]

Options

A. `36^(@)` C
B. `83^(@)` C
C. `63^(@) C`
D. `33^(@) C`

Answer

B

Explanation

`R_(1) = 10 Omega, R_(2) = 10 + 10 xx 10/100 = 11 Omega`
`R_(1)/R_(2) = (1 + alpha xx 30)/(1 + alpha xx t) rArr 10/11 = (1 + 0.002 xx 30)/(1 + 0.0.002 xx t)`
`rArr 10 + 0.02t = 11 + 0.002 xx 30 xx 11`
`rArr t = 83^(@)` C