H = ISq RT
heat is directly proportional to the square of current,resistance of the wire and temperature when currebt flows in a wire.

Introduction

When an electric current flows through a conductor, heat is produced due to the resistance of the conductor. This phenomenon is known as Joule heating. The heat produced in a conductor can be calculated using the formula:

H = I^2 * R * t

Where:
H = heat produced (in Joules)
I = current flowing through the conductor (in Amperes)
R = resistance of the conductor (in Ohms)
t = time for which the current flows through the conductor (in seconds)

Explanation

The heat produced in a conductor is directly proportional to the square of the current flowing through it, the resistance of the conductor, and the time for which the current flows. This relationship is expressed by the formula mentioned above.

The heat produced in a conductor can be understood by considering the behavior of electrons in the conductor. When a current flows through a conductor, the electrons move through the conductor, colliding with the atoms or molecules of the conductor. These collisions result in the transfer of energy from the moving electrons to the conductor, which leads to the generation of heat.

Derivation of the formula

To derive the formula for heat produced in a conductor, we can start with Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance:

I = V/R

Where:
I = current flowing through the conductor (in Amperes)
V = voltage across the conductor (in Volts)
R = resistance of the conductor (in Ohms)

We can rearrange this equation to solve for V:

V = I * R

Now, we can substitute this value of V in the formula for power:

P = V * I

Where:
P = power (in Watts)

Substituting the value of V from the rearranged equation, we get:

P = (I * R) * I

Simplifying further, we have:

P = I^2 * R

Since power is the rate at which heat is produced, we can rewrite the formula as:

H = I^2 * R * t

Where:
H = heat produced (in Joules)
t = time for which the current flows through the conductor (in seconds)

Conclusion

In conclusion, the heat produced in a conductor when a current flows through it can be calculated using the formula H = I^2 * R * t. This formula takes into account the current flowing through the conductor, the resistance of the conductor, and the time for which the current flows. Understanding and calculating the heat produced in a conductor is important in various practical applications, such as designing electrical circuits and calculating energy consumption.