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A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2 is constant and the loop rotates about the x-axis with a frequency of 50 Hz?
- a)32.65 volts
- b)18.54 volts
- c)28 volts
- d)25.13 volts
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A rectangular loop of length a = 1 meter and width b = 80 cm is placed...
The induced emf in uniform magnetic field is given by
v = ω(ab) B sin ωt
or, v = ωAB sin ωt
(where, A = ab = Area of rectangular loop)
or
v = ω(ab) B sin ωt
or, v = ωAB sin ωt
(where, A = ab = Area of rectangular loop)
or
Most Upvoted Answer
A rectangular loop of length a = 1 meter and width b = 80 cm is placed...
Given data:
- Length of the loop (a) = 1 meter
- Width of the loop (b) = 80 cm = 0.8 meters
- Magnetic flux density (B) = 0.1 Wb/m^2
- Frequency of rotation (f) = 50 Hz
Calculating the maximum induced emf:
- The maximum induced emf (ε) can be calculated using the formula:
ε = B * A * ω * sin(θ)
where A is the area of the loop and θ is the angle of rotation.
Calculating the area of the loop:
- Area (A) = a * b = 1 * 0.8 = 0.8 m^2
Calculating the angular frequency:
- Angular frequency (ω) = 2πf = 2 * π * 50 = 100π rad/s
Calculating the maximum induced emf:
- ε = 0.1 * 0.8 * 100π * sin(θ)
- As sin(θ) has a maximum value of 1, the maximum induced emf occurs when sin(θ) = 1
- Therefore, the maximum induced emf (ε_max) = 0.1 * 0.8 * 100π * 1 = 25.13 volts
Therefore, the maximum value of induced emf when the loop rotates about the x-axis with a frequency of 50 Hz in a constant magnetic field of 0.1 Wb/m^2 is 25.13 volts. Option D is the correct answer.
- Length of the loop (a) = 1 meter
- Width of the loop (b) = 80 cm = 0.8 meters
- Magnetic flux density (B) = 0.1 Wb/m^2
- Frequency of rotation (f) = 50 Hz
Calculating the maximum induced emf:
- The maximum induced emf (ε) can be calculated using the formula:
ε = B * A * ω * sin(θ)
where A is the area of the loop and θ is the angle of rotation.
Calculating the area of the loop:
- Area (A) = a * b = 1 * 0.8 = 0.8 m^2
Calculating the angular frequency:
- Angular frequency (ω) = 2πf = 2 * π * 50 = 100π rad/s
Calculating the maximum induced emf:
- ε = 0.1 * 0.8 * 100π * sin(θ)
- As sin(θ) has a maximum value of 1, the maximum induced emf occurs when sin(θ) = 1
- Therefore, the maximum induced emf (ε_max) = 0.1 * 0.8 * 100π * 1 = 25.13 volts
Therefore, the maximum value of induced emf when the loop rotates about the x-axis with a frequency of 50 Hz in a constant magnetic field of 0.1 Wb/m^2 is 25.13 volts. Option D is the correct answer.
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A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer?
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A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer?.
A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rectangular loop of length a = 1 meter and width b = 80 cm is placed in a uniform magnetic field. What is the maximum value of induced emf if the magnetic flux density B - 0.1 Wb/m2is constant and the loop rotates about the x-axis with a frequency of 50 Hz?a)32.65 voltsb)18.54 voltsc)28 voltsd)25.13 voltsCorrect answer is option 'D'. Can you explain this answer?.
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