If the current increases by a factor of 3 in Joule's Law, by what factor does the heat energy q increase?

• A. Increases by factor 3
• B. Increases by factor 9
• C. Decreases by factor 3
• D. Stays the same

Answer: (B)

Heat produced in a resistor over time follows Joule’s law, which shows q is proportional to I squared when resistance and time are fixed: q ∝ I^2. Using q = I^2 R t, if the current goes up by a factor of 3, the heat energy scales by 3^2, which is 9. So the heat energy becomes nine times larger. (This square relationship is the reason the factor is nine; other quantities like resistance or duration would change the result if they weren’t fixed.)