State Joules law of heating . write the mathematical form of this law .?

Question

Answer

Joule's law is given by:  Q = I^2Rt Corresponding units: joules(J) = ampere2(A2) · ohm(Ω) · second(s)  Where:  Q is the heat generated I is the current(constant) R is the resistance of the conductor t is the time   The unit of the heat generated is joule, which can be rewritten as:  joule = kg · m2 / s2

Answer

*According to the Joule’s law of heating, heat produced in a resistor is directly proportional to the:

*(i) square of current for a given resistance.

*(ii) resistance for a given current.

*(iii)the time for which the current flows through the resistor.

*mathematical formula for this law is H = I^2Rt.

Answer

Joule's law of heating, also known as the Joule heating effect, states that the amount of heat produced in a conductor is directly proportional to the square of the current passing through it, the resistance of the conductor, and the time for which the current flows. This law is named after James Prescott Joule, a British physicist who conducted experiments to determine the relationship between electrical energy and heat.

Mathematical Form:
The mathematical form of Joule's law of heating is given by the equation:

H = I^2 * R * t

Where:
H is the amount of heat produced (in joules),
I is the current flowing through the conductor (in amperes),
R is the resistance of the conductor (in ohms), and
t is the time for which the current flows (in seconds).

Explanation:
1. Introduction:
Joule's law of heating is based on the principle that when an electric current passes through a conductor, it encounters resistance. This resistance causes the electrical energy to be converted into heat energy.

2. Relationship between Heat, Current, Resistance, and Time:
According to Joule's law, the amount of heat produced is directly proportional to the square of the current, the resistance of the conductor, and the time for which the current flows. This means that if any of these factors increase, the heat produced will also increase.

3. Current (I):
The current flowing through a conductor is the rate of flow of electric charge. It is measured in amperes (A). The greater the current passing through the conductor, the more heat will be produced.

4. Resistance (R):
Resistance is a measure of how difficult it is for the current to flow through a conductor. It is measured in ohms (Ω). A higher resistance means that more heat will be produced as the current encounters greater opposition.

5. Time (t):
The time for which the current flows through the conductor also affects the amount of heat produced. The longer the time, the more heat will be generated.

6. Square Relationship:
The square relationship in Joule's law indicates that the heat produced is directly proportional to the square of the current. This means that even a small increase in current can significantly increase the amount of heat generated.

7. Practical Applications:
Joule's law of heating finds numerous practical applications. It is used in electric heaters, electric stoves, incandescent light bulbs, and other devices where electrical energy is converted into heat.

In conclusion, Joule's law of heating states that the amount of heat produced in a conductor is directly proportional to the square of the current, resistance, and time. This law provides a fundamental understanding of the relationship between electrical energy and heat and has significant applications in various electrical devices.

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