If resistance of conductor is R then total heat dissipated across resistance R is

When a current flows through a conductor with resistance R, it generates heat due to the collisions between the moving charge carriers (like electrons) and the atoms in the conductor. This phenomenon is described by Joule's law, which tells us how much heat is produced in a conductor when an electric current passes through it.

The Relationship Between Resistance, Current, and Heat

The total heat dissipated (Q) across a resistance R can be calculated using the formula:

• Q = I²RT

In this equation:

• Q is the amount of heat produced (measured in joules)
• I represents the current flowing through the conductor (in amperes)
• R is the resistance of the conductor (in ohms)
• T is the time for which the current flows (in seconds)

Breaking Down the Formula

This formula essentially shows that the heat generated is directly proportional to the square of the current, the resistance, and the time duration of current flow. Let’s look at how this works with an example:

Example Scenario

Imagine you have a resistor with a resistance of 10 ohms, and a current of 2 amperes flowing through it for 5 seconds. Plugging these values into the formula:

• R = 10 ohms
• I = 2 amperes
• T = 5 seconds

Now, calculate the heat:

• Q = (2)² * 10 * 5
• Q = 4 * 10 * 5
• Q = 200 joules

This means that during the 5 seconds, the resistor dissipates 200 joules of heat energy.

Why This Matters

Understanding this concept is crucial in various fields, such as electrical engineering and physics, as it helps in designing circuits and ensuring components do not overheat. Excessive heat can lead to failure of electronic devices, so knowing how to calculate heat dissipation allows engineers to create safer and more efficient systems.

In summary, the heat dissipated across a resistance R when a current flows through it can be calculated using the formula Q = I²RT, illustrating the relationship between electrical current, resistance, and time. This knowledge is essential for safe and effective electrical design and applications.

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