JEE Main 2023 · 31 January · evening · Single correct · +4 / −1
The H amount of thermal energy is developed by a resistor in 10 s when a current of 4 A is passed through it. If the current is increased to 16 A, the thermal energy developed by the resistor in 10 s will be :
- (a) H/4
- (b) 16 H
- (c) H
- (d) 4 H
Answer and solution
Answer (b) 16 H
Solution
Physics sir · 3 steps
Heat goes as current squared, so making the current 4 times larger makes the heat 16 times larger.
- Joule heating. The heat produced in a resistor is H = I² R t. Here R is the same resistor and t = 10 s both times, so only I changes.
H'/H = (I'/I)² = (16/4)² = 16
- Why squared. A bigger current carries more charge per second, and each charge also loses more energy because the voltage IR is larger. Two factors of I give I².
- So. H' = 16H, which is option (b).
The idea to keep. For a fixed resistor and fixed time, heat scales as I². Find the ratio of the currents and square it; do not stop at the plain ratio.
Answer from the NTA final answer key. Solution by PrepWiser.