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Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double?
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Derive an equation for heat produced in a conductor of resistance R,wh...
Deriving the Heat Equation
When a current flows through a conductor, heat is produced due to the resistance of the material. The heat produced (H) can be derived using Joule's Law, which states that the heat generated is directly proportional to the square of the current, the resistance, and the time for which the current flows.
The equation for heat produced in a conductor is given by:
H = I²RT
Where:
- H = Heat produced (in Joules)
- I = Current (in Amperes)
- R = Resistance (in Ohms)
- T = Time (in seconds)
Effect of Doubling Current
When the current (I) is doubled, the new current becomes 2I. Substituting this into the original heat equation gives us:
H' = (2I)²RT
This simplifies to:
H' = 4I²RT
From this, we can see that:
- The heat produced when the current is doubled becomes four times the original heat produced.
- H' = 4H
Conclusion
- Heat Generation: The heat generated in a conductor is proportional to the square of the current.
- Doubling Current: If the current is doubled, the heat produced increases by a factor of four.
- Implication: This relationship illustrates the significant impact of current on heat generation in electrical conductors, emphasizing the need for careful consideration in electrical design to prevent overheating.
Understanding these principles is crucial for applications in electrical engineering and safety in circuit design.
When a current flows through a conductor, heat is produced due to the resistance of the material. The heat produced (H) can be derived using Joule's Law, which states that the heat generated is directly proportional to the square of the current, the resistance, and the time for which the current flows.
The equation for heat produced in a conductor is given by:
H = I²RT
Where:
- H = Heat produced (in Joules)
- I = Current (in Amperes)
- R = Resistance (in Ohms)
- T = Time (in seconds)
Effect of Doubling Current
When the current (I) is doubled, the new current becomes 2I. Substituting this into the original heat equation gives us:
H' = (2I)²RT
This simplifies to:
H' = 4I²RT
From this, we can see that:
- The heat produced when the current is doubled becomes four times the original heat produced.
- H' = 4H
Conclusion
- Heat Generation: The heat generated in a conductor is proportional to the square of the current.
- Doubling Current: If the current is doubled, the heat produced increases by a factor of four.
- Implication: This relationship illustrates the significant impact of current on heat generation in electrical conductors, emphasizing the need for careful consideration in electrical design to prevent overheating.
Understanding these principles is crucial for applications in electrical engineering and safety in circuit design.
Community Answer
Derive an equation for heat produced in a conductor of resistance R,wh...
heat increase 4 times
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Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double?
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Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double?.
Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Derive an equation for heat produced in a conductor of resistance R,when a current I flows for time T. What happens to the heat produced when current becomes double?.
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