A `2^(@)C` rise in temperature is observed in a conductor passing a current. When the current is tripled. The rise in temperature will be

Options

A. `9^(@)C`
B. `18^(@)C`
C. `27^(@)C`
D. `36^(@)C`

Answer

2

Explanation

Heat developed in a conductor due to current =`I^(2)Rt`.
Amount of heat energy in raising temperature of the conductor =mc`Deltatheta`
Since, the heat developed in the conductor is used in raising the temperature of the conductor.
`therefore I^(2)Rt=mcDeltatheta` or `Delta thetapropI^(2)`
`(Deltatheta_(1))/(Deltatheta_(2))=(I_(1)^(2))/(I_(2)^(2))`
or `Delta theta_(2)=Delta theta_(1)((I_(2))/(I_(1)))^(2)=Deltatheta_(1)((3I)/(I))^(2)`
`=Deltatheta_(1)xx18^(@)C,(because Deltatheta_(1)=2^(@)C)`