How much heat is produced in a resistor having a resistance of R ohms when a current of I amperes is passed through it for t seconds?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(I^2Rt\) joule
By Joule's law of heating, the work done in driving a current through a resistor is all turned into heat. A current \(I\) for time \(t\) carries a charge \(It\) through the potential difference \(V\):
Heat \(H=V\times It\)
With \(V=IR\) (Ohm's law): \(H=I^2Rt\) joule
Why the other options are incorrect
Option (1) \(I^2/R\) joule — Incorrect. It divides by R and leaves out the time; heat grows with both R and t.
Option (2) \(V^2/R\) joule — Incorrect. \(V^2/R\) is the power, the heat produced each second, in watts; it must be multiplied by t.
Option (4) \(IRt\) joule — Incorrect. \(IRt\) is only \(Vt\); it lacks one factor of I, so it is not an energy.