A resistor develops 200 J of thermal energy in 5 s when a current of 2 A is passed through it. If the current is increased to 5 A, what will be the energy developed in 12 s?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3000 J
By Joule's law of heating the thermal energy developed in a resistor R carrying a current I for a time t is \( H = I^{2}Rt \). First find R from the first case, then use it in the second.
\( \displaystyle R = \frac{H}{I^{2}t} = \frac{200}{(2)^{2}\times5} = 10\,\Omega \)
\( H' = I'^{2}Rt' = (5)^{2}\times10\times12\,\mathrm{J} = 3000\,\mathrm{J} \)