Question

If the electric current passing through a fixed resistor is halved, then the heat produced in it will become

• A. double
• B. half
• C. one-fourth
• D. four times

Hint:

Joule's Law states that the heat produced by a current is directly proportional to the square of the current. Halving the current reduces the heat produced by a factor of four.

Answer 1

The Correct Option is C

Step 1: Understanding Joule's Law of Heating
The heat produced due to a current passing through a resistor is given by Joule's Law: \[ H = I^2 R t \] where: - \(H\) is the heat produced
- \(I\) is the current
- \(R\) is the resistance
- \(t\) is the time for which the current flows

Step 2: Halving the Current
If the current \(I\) is halved, the new current becomes \( \frac{I}{2} \). According to Joule's law, the heat produced will now be: \[ H' = \left(\frac{I}{2}\right)^2 R t = \frac{I^2}{4} R t = \frac{1}{4} H \] Thus, the heat produced is one-fourth of the original heat when the current is halved.

Step 3: Conclusion
Thus, the heat produced when the current is halved becomes one-fourth. The correct answer is option (C).