Question

When a current is passed in a conductor, 3$^{\circ}$C rise in temperature is observed. If the strength of current is made thrice, then rise in temperature will approximately be

• A. 36$^{\circ}$C
• B. 27$^{\circ}$C
• C. 18$^{\circ}$C
• D. 9$^{\circ}$C

Answer 1

The Correct Option is B

$H=I^{2} R t=m c \Delta \theta$ $\therefore \Delta \theta \propto I^{2}$ Hence $\frac{\Delta \theta_{2}}{\Delta \theta_{1}}=\left(\frac{I_{2}}{I_{1}}\right)^{2}$ or $\frac{\Delta \theta_{2}}{3}=\left(\frac{3 I}{I}\right)^{2}$ or $\Delta \theta_{2}=9 \times 3=27^{\circ} C$