A resistor dissipates 192 J of energy in 1s when a current of 4A is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in 5s in _________ J.

Solution

Physics sir · 3 steps

Heat goes as I², so doubling the current makes the power four times bigger. Then multiply by 5 s.

1. Find the resistance. In 1 s the resistor gives out 192 J, so its power is P = 192 W. From P = I² R, R = 192/4² = 192/16 = 12 Ω.
2. New power. With the current doubled to 8 A and the same resistor, P = 8² × 12 = 64 × 12 = 768 W. That is 4 times the old 192 W.

   H = I² R t = 8² × 12 × 5

3. So. H = 768 × 5 = 3840 J, so the answer is 3840.

The common slip: 1920. Treating heat as proportional to I instead of I² makes the power 384 W, which gives 1920 J in 5 s, not 3840.

The idea to keep. For a fixed resistor, Joule heating H = I² R t goes as the square of the current. Double I and the heat per second becomes four times as much.

Answer from the NTA final answer key. Solution by PrepWiser.