A resistor develops 500 J of thermal energy in 20 s when a current of 1.5A is passed through it. If the current is increased from 1.5A to 3A, what will be the energy developed in 20 s.

Solution

Physics sir · 3 steps

Same resistor, same time: heat goes as current squared, so doubling I makes it four times.

1. Heat in a resistor. Joule heating gives H = I² R t. Here R and t stay the same, so H depends only on I².

   H₂/H₁ = (I₂/I₁)² = (3/1.5)² = 4

2. Put in numbers. H₂ = 4 × 500 J = 2000 J.
3. So. The resistor develops 2000 J in 20 s, which is option (b).

The idea to keep. For a fixed resistor, heat goes as I². Double the current and the heat becomes four times, not two times. Compare ratios and you never need R itself.

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