Why do we consider heat directly proportional to resistance and not inversely proportional, since we know the relation (H=I^2RT) and also (H=V^2/R)?

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According joules law heat produced in the conductor is  directly proportional square of the current flowing

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See heat is inversely proportional to R in second case because there the V is constant....

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Heat and Resistance: Direct Proportionality Explanation

Introduction:
When it comes to the relationship between heat and resistance, it is important to understand the underlying principles of Ohm's Law. Ohm's Law states that the current passing through a conductor is directly proportional to the voltage applied across it and inversely proportional to the resistance of the conductor. However, the relationship between heat and resistance is different and can be explained by the power law.

Power Law:
The power law equation, which relates power (heat) to current, resistance, and voltage, is given by:
H = I^2 * R * T
where H is the heat generated, I is the current flowing through the conductor, R is the resistance of the conductor, and T is the time.

Explanation:
1. Direct Proportionality:
The equation H = I^2 * R * T clearly shows that the heat generated is directly proportional to the resistance of the conductor. This means that as the resistance increases, the heat generated also increases, and vice versa. The direct proportionality between heat and resistance can be understood by considering the following points:

- When the resistance of a conductor increases, it restricts the flow of current. As a result, the energy carried by the electrons is converted into heat energy, leading to an increase in heat generation.
- Similarly, when the resistance decreases, the flow of current increases, resulting in a decrease in heat generation.

2. Inverse Proportionality:
Although Ohm's Law states that current is inversely proportional to resistance, this inverse relationship does not directly translate to the relationship between heat and resistance. The reason for this is that the power equation considers the square of the current (I^2), which results in a direct proportionality between heat and resistance.

Conclusion:
In conclusion, the relationship between heat and resistance is best described as a direct proportionality. This can be explained by the power law equation, which considers the current squared (I^2). As the resistance of a conductor increases, the heat generated also increases, and as the resistance decreases, the heat generated decreases. Understanding this relationship is crucial in various fields, such as electrical engineering, where managing heat dissipation is essential for the proper functioning and longevity of electronic components and circuits.

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