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: Understanding the Question:
The question asks which physical quantity is directly proportional to the generated heat in a conductor when the current passing through it is kept constant, according to Joule's law of heating.

Step 2: Key Formula or Approach:
Joule's law of heating states that the heat energy (\(H\)) generated in a conductor is given by:
\[ H = I^2 R t \]
where:
\(I\) is the constant electric current,
\(R\) is the electrical resistance of the conductor,
\(t\) is the time duration for which the current flows.

Step 3: Detailed Explanation:

• From the relation \(H = I^2 R t\), we can observe three direct proportionalities:
1. Heat is directly proportional to the square of the current (\(H \propto I^2\)) for a given resistance and time.
2. Heat is directly proportional to the resistance of the conductor (\(H \propto R\)) for a constant current and time.
3. Heat is directly proportional to the time duration of current flow (\(H \propto t\)) for a given current and resistance.

• The question specifies that the current \(I\) remains constant.

• Under this condition, \(H\) is directly proportional to the resistance \(R\) (and time \(t\)).

• Looking at the options, "The resistance" is the correct factor.


Step 4: Final Answer:
Thus, the heat produced is directly proportional to the resistance of the conductor.