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. 86°C
C. 63°C
D. 33°C

Answer

B

Explanation

`R_(t) = R_(0) ( 1+ alphat )`.
Initially, `R_(0) (1+ 30 alpha) = 10 Omega`
Finally, `R_0 ( 1+ alpha t) = 11 Omega`
`therefore (11)/(10) = (1+ alpha t)/( 1 + 30 alpha)`
or, `10 + (10 xx 0.002 xx t) = 11+ 330 xx 0.002`
or, `0.02 t = 1+ 0.66 = 1.066` or `t= (1.66)/(0.02) = 86^(@) C`