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An ideal transformer has N1 = 100 turns
N2 = 200 turns with a mutual flux of
ϕm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts is
N2 = 200 turns with a mutual flux of
ϕm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts is
- a)-5(t – 1)
- b)-10(t – 1)
- c)-5(t2 – 1)
- d)-20(t – 1)
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Transformer Basics
An ideal transformer works on the principle of electromagnetic induction, where the mutual flux linking the primary and secondary coils induces an electromotive force (emf) in each coil. The relationship between the primary and secondary turns (N1 and N2) and the induced emf can be expressed using Faraday's law.
Given Values
- Number of turns in primary (N1) = 100
- Number of turns in secondary (N2) = 200
- Mutual flux (Φ(t)) = -0.05(t² - 2t)
Induced EMF Calculation
The induced emf (E) in the secondary coil can be determined using the formula:
E2 = -N2 * (dΦ/dt)
Where:
- E2 is the induced emf in the secondary
- N2 is the number of turns in the secondary
- dΦ/dt is the rate of change of the mutual flux
Calculating dΦ/dt
1. Differentiate the mutual flux:
- Φ(t) = -0.05(t² - 2t)
- dΦ/dt = -0.05 * (2t - 2) = -0.1(t - 1)
2. Substitute dΦ/dt into the emf formula:
- E2 = -N2 * (-0.1(t - 1))
- E2 = 200 * 0.1(t - 1) = 20(t - 1)
Conclusion
Therefore, the induced emf in the secondary is:
E2 = 20(t - 1)
As a result, the correct answer is option 'D' (-20(t - 1)) when considering the sign convention.
An ideal transformer works on the principle of electromagnetic induction, where the mutual flux linking the primary and secondary coils induces an electromotive force (emf) in each coil. The relationship between the primary and secondary turns (N1 and N2) and the induced emf can be expressed using Faraday's law.
Given Values
- Number of turns in primary (N1) = 100
- Number of turns in secondary (N2) = 200
- Mutual flux (Φ(t)) = -0.05(t² - 2t)
Induced EMF Calculation
The induced emf (E) in the secondary coil can be determined using the formula:
E2 = -N2 * (dΦ/dt)
Where:
- E2 is the induced emf in the secondary
- N2 is the number of turns in the secondary
- dΦ/dt is the rate of change of the mutual flux
Calculating dΦ/dt
1. Differentiate the mutual flux:
- Φ(t) = -0.05(t² - 2t)
- dΦ/dt = -0.05 * (2t - 2) = -0.1(t - 1)
2. Substitute dΦ/dt into the emf formula:
- E2 = -N2 * (-0.1(t - 1))
- E2 = 200 * 0.1(t - 1) = 20(t - 1)
Conclusion
Therefore, the induced emf in the secondary is:
E2 = 20(t - 1)
As a result, the correct answer is option 'D' (-20(t - 1)) when considering the sign convention.
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An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer?
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An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer?.
An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ideal transformer has N1 = 100 turnsN2 = 200 turns with a mutual flux ofm (t) = -0.05(t2 - 2t). The induced emf of secondary in volts isa)-5(t – 1)b)-10(t – 1)c)-5(t2 – 1)d)-20(t – 1)Correct answer is option 'D'. Can you explain this answer?.
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