Question

In Joule's law of heating, the heat produced is directly proportional to which factor when the current remains constant?

• A. The square of the time
• B. The resistance
• C. The length of the wire
• D. The temperature

Hint:

Always look at the variable held constant.
If current (\(I\)) is constant, use \(H = I^2 R t\) (\(H \propto R\)).
If voltage (\(V\)) is constant, use \(H = \frac{V^2}{R} t\) (\(H \propto \frac{1}{R}\)).

Answer 1

The Correct Option is B

Step 1: Write down Joule's heating law.
The heat generated in a resistor over time \(t\) is \[ H = I^2 R t \]
Step 2: Freeze the current.
The question tells us current \(I\) is held constant, so \(I^2\) becomes just a fixed number multiplying the rest of the expression. What remains free to vary is \(R\) and \(t\).
Step 3: Read off the proportionality.
With \(I\) fixed and looking at a given time interval, \(H\) simply scales up and down with \(R\), doubling \(R\) doubles the heat produced. That is a direct proportionality between heat and resistance.
\[ \boxed{H \propto R \text{ when } I \text{ is constant}} \]