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A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be
- a)halved
- b)the same
- c)doubled
- d)quadrupled
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A short-circuited coil is placed in a time-varying magnetic field. Ele...
KEY CONCEPT :
NOTE : When we decrease the radius of the wire, its length increases but volume remains the same]
∴ Power remains the same.
Most Upvoted Answer
A short-circuited coil is placed in a time-varying magnetic field. Ele...
Explanation:
When a coil is placed in a time-varying magnetic field, an EMF is induced in the coil that results in the flow of current. The power dissipated in the coil is given by P = I^2R, where I is the current flowing through the coil and R is the resistance of the coil. The resistance of the coil is given by R = (ρl)/A, where ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.
Effect of changing the number of turns:
If the number of turns in the coil is quadrupled, the EMF induced in the coil will be four times greater than before. However, the resistance of the coil will also increase fourfold since the length of wire will increase accordingly. Therefore, the current flowing through the coil will remain the same. As a result, the power dissipated in the coil will remain the same as well.
Effect of changing the wire radius:
If the wire radius is halved, the cross-sectional area of the wire will decrease by a factor of four. As a result, the resistance of the coil will increase fourfold. However, the EMF induced in the coil will remain the same since the magnetic field and the number of turns have not changed. Therefore, the current flowing through the coil will decrease by a factor of two. As a result, the power dissipated in the coil will remain the same as well.
Conclusion:
The change in the number of turns and wire radius will have opposite effects on the power dissipated in the coil. The increase in the number of turns will increase the EMF induced in the coil, while the increase in wire radius will decrease the current flowing through the coil. However, these effects cancel each other out, and the power dissipated in the coil will remain the same. Therefore, the correct answer is option B.
When a coil is placed in a time-varying magnetic field, an EMF is induced in the coil that results in the flow of current. The power dissipated in the coil is given by P = I^2R, where I is the current flowing through the coil and R is the resistance of the coil. The resistance of the coil is given by R = (ρl)/A, where ρ is the resistivity of the material, l is the length of the wire, and A is the cross-sectional area of the wire.
Effect of changing the number of turns:
If the number of turns in the coil is quadrupled, the EMF induced in the coil will be four times greater than before. However, the resistance of the coil will also increase fourfold since the length of wire will increase accordingly. Therefore, the current flowing through the coil will remain the same. As a result, the power dissipated in the coil will remain the same as well.
Effect of changing the wire radius:
If the wire radius is halved, the cross-sectional area of the wire will decrease by a factor of four. As a result, the resistance of the coil will increase fourfold. However, the EMF induced in the coil will remain the same since the magnetic field and the number of turns have not changed. Therefore, the current flowing through the coil will decrease by a factor of two. As a result, the power dissipated in the coil will remain the same as well.
Conclusion:
The change in the number of turns and wire radius will have opposite effects on the power dissipated in the coil. The increase in the number of turns will increase the EMF induced in the coil, while the increase in wire radius will decrease the current flowing through the coil. However, these effects cancel each other out, and the power dissipated in the coil will remain the same. Therefore, the correct answer is option B.
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A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer?
Question Description
A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer?.
A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would bea)halvedb)the samec)doubledd)quadrupledCorrect answer is option 'B'. Can you explain this answer?.
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