Question:
A coil with "I" amperes of current and "R" ohm resistance and "t" is time in second, the heat produced 'H' in joules is given by which of the following equation ?
A coil with "I" amperes of current and "R" ohm resistance and "t" is time in second, the heat produced 'H' in joules is given by which of the following equation ?
Show Hint
Joule heating is also known as "resistive heating" or "\( I^2 R \)" losses.
Because heat generation increases with the square of the current, doubling the current increases the heat produced by a factor of four.
Because heat generation increases with the square of the current, doubling the current increases the heat produced by a factor of four.
Updated On: Jul 21, 2026
- H = I\(^{2}\)Rt
- H = I\(^{2}\)R\(^{2}\)t
- H = IR\(^{2}\)t
- H = I\(^{2}\)R\(^{2}\)/t
Show Solution
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
When an electric current flows through a conductor with electrical resistance, the conductor resists the flow of charge, converting some electrical energy into thermal energy.
Detailed Explanation:
This conversion of electrical energy to heat is governed by Joule's Law of Heating.
According to this law, the heat generated (\( H \)) in a conductor is:
1. Directly proportional to the square of the electric current (\( I^2 \)).
2. Directly proportional to the electrical resistance of the conductor (\( R \)).
3. Directly proportional to the time duration (\( t \)) for which the current flows.
Combining these proportionalities yields the equation:
\[ H = I^2 \cdot R \cdot t \text{ Joules} \] Let us derive this from Ohm's Law and the definition of power:
- Electrical Power (\( P \)) is:
\[ P = V \cdot I \] - Substituting Ohm's Law (\( V = I \cdot R \)) into the power equation:
\[ P = (I \cdot R) \cdot I = I^2 R \] - Total heat energy generated (\( H \)) over time \( t \) is power multiplied by time:
\[ H = P \cdot t = I^2 R t \] This matches the equation in Option (A).
Step 2: Final Answer:
The heat produced is given by the equation \( H = I^2 R t \).
When an electric current flows through a conductor with electrical resistance, the conductor resists the flow of charge, converting some electrical energy into thermal energy.
Detailed Explanation:
This conversion of electrical energy to heat is governed by Joule's Law of Heating.
According to this law, the heat generated (\( H \)) in a conductor is:
1. Directly proportional to the square of the electric current (\( I^2 \)).
2. Directly proportional to the electrical resistance of the conductor (\( R \)).
3. Directly proportional to the time duration (\( t \)) for which the current flows.
Combining these proportionalities yields the equation:
\[ H = I^2 \cdot R \cdot t \text{ Joules} \] Let us derive this from Ohm's Law and the definition of power:
- Electrical Power (\( P \)) is:
\[ P = V \cdot I \] - Substituting Ohm's Law (\( V = I \cdot R \)) into the power equation:
\[ P = (I \cdot R) \cdot I = I^2 R \] - Total heat energy generated (\( H \)) over time \( t \) is power multiplied by time:
\[ H = P \cdot t = I^2 R t \] This matches the equation in Option (A).
Step 2: Final Answer:
The heat produced is given by the equation \( H = I^2 R t \).
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