Relationship between Resistance and Heat:
Resistance is the opposition to the flow of electric current in a material. It is determined by the material's properties such as its length, cross-sectional area, and temperature. The relationship between resistance and heat can be explained as follows:

Directly Proportional:
- In most materials, resistance is directly proportional to heat. This means that as the temperature of a material increases, its resistance also increases.
- This is due to the fact that as the material heats up, its atoms and molecules vibrate more vigorously, causing more collisions with the flowing electrons and increasing the overall resistance to current flow.
- This phenomenon is known as the positive temperature coefficient of resistance, and it is commonly observed in metals and semiconductors.

Inversely Proportional:
- However, there are some materials, such as superconductors, where resistance is inversely proportional to heat. These materials exhibit zero resistance at very low temperatures.
- In superconductors, as the temperature decreases, the resistance also decreases until it reaches zero at a critical temperature known as the transition temperature.
- This phenomenon is known as the negative temperature coefficient of resistance, and it is a unique property of superconducting materials.

Conclusion:
In general, resistance is directly proportional to heat in most materials, but there are exceptions such as superconductors where resistance is inversely proportional to heat. Understanding this relationship is crucial for various applications in electronics, power transmission, and material science.