Question

When a current is passed in a conductor, 3${}^{o}C$ rise in temperature is observed. If the strength of current is increased three times, then rise in temperature will approximately be:

• A. $3^{o}C$
• B. $9^{o}C$
• C. ${27}^{o}C$
• D. ${36}^{o}C$

Answer 1

The correct option is C ${27}^{o}C$

When a current is passed in a conductor, it produces the heat and increases the temperature. Heat produced in a conductor is equivalent to rise in temperature.
As per the problem,
$H_1=(I_1{)}^{2}R$ ...............(1)
where, variables have their usual meanings.
$H_2=(3I_1{)}^{2}R$
$H_2=9(I_1{)}^{2}R$
$H_2=9H_1$ ...............from (1)

Since $H\propto \Delta T$ $\Delta T_2=27{}^{o}C$