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Two coupled coils with L1 = 0.5 H and L2 = 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1 = 20 sin 314t A is passed in coil 1.
- a)22.6 V
- b)444 V
- c)7.1 kV
- d)355 V
Correct answer is option 'C'. Can you explain this answer?
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Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of ...
Concept:
Self-inductance is the property of the current-carrying coil that resists or opposes the change of current flowing through it. This occurs mainly due to the self-induced emf produced in the coil itself. In simple terms, we can also say that self-inductance is a phenomenon where there is the induction of a voltage in a current-carrying wire.
Self-inductance, usually just called inductance, L is the ratio between the induced voltage and the rate of change of the current
V1(t) = L (di1/dt)
Mutual Inductance between the two coils is defined as the property of the coil due to which it opposes the change of current in the other coil, or you can say in the neighboring coil. When the current in the neighboring coil changes, the flux sets up in the coil and, because of this, changing flux emf is induced in the coil called Mutually Induced emf and, the phenomenon is known as Mutual Inductance.
V2(t) = M (di1/dt)
Coefficient of Coupling:
The amount of coupling between the inductively coupled coils is expressed in terms of the coefficient of coupling, which is defined as
where M = mutual inductance between the coils
L1 = self-inductance of the first coil, and
L2 = self-inductance of the second coil
- The coefficient of coupling is always less than unity and has a maximum value of 1 (or 100%).
- This case, for which K = 1, is called perfect coupling when the entire flux of one coil links the other.
- The greater the coefficient of coupling between the two coils, the greater the mutual inductance between them, and vice-versa.
Calculations:
Given
L1 = 0.5 H
L2 = 4 H
K = 0.8
I = 20 sin 314t
The induced emf in coil 2 due to current in coil 1 is given by
V2 = M (di1 / dt)
M = 1.13 H
V2 = 1.13 d/dt (20 sin 314t)
V2 = 1.13 × 20 × 314 × cos 314t
The maximum value of V2 = 1.13 × 20 × 314 = 7.1 kV
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Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of ...
Given data:
L1 = 0.5 H (inductance of coil 1)
L2 = 4.0 H (inductance of coil 2)
k = 0.8 (coefficient of coupling)
i1 = 20 sin 314t A (current through coil 1)
To find:
Maximum value of the induced EMF in coil 2.
Formula:
The mutual inductance (M) between two coils is given by:
M = k * sqrt(L1 * L2)
The induced EMF in the second coil is given by:
e2 = -M * di1/dt
where di1/dt is the rate of change of current through coil 1.
Calculation:
Using the formula for mutual inductance, we can calculate the value of M as follows:
M = k * sqrt(L1 * L2)
= 0.8 * sqrt(0.5 * 4.0)
= 0.8 * sqrt(2.0)
≈ 0.8 * 1.414
≈ 1.131 H
Since the current through coil 1 is given by i1 = 20 sin 314t A, we can calculate the rate of change of current as follows:
di1/dt = d/dt (20 sin 314t)
= 20 * d/dt (sin 314t)
= 20 * 314 * cos 314t A/s
The maximum value of cos 314t is 1, so we can substitute this value to calculate the maximum rate of change of current:
di1/dt = 20 * 314 * 1
= 6280 A/s
Finally, we can calculate the maximum value of the induced EMF in coil 2 using the formula:
e2 = -M * di1/dt
= -1.131 * 6280 V
≈ -7091.48 V
The negative sign indicates that the induced EMF in coil 2 is in the opposite direction to the change in current in coil 1.
Since the maximum value of the induced EMF is given as a positive value, we take the absolute value:
|e2| ≈ 7091.48 V
Therefore, the maximum value of the induced EMF in coil 2 is approximately 7.1 kV (kilovolts). Hence, the correct answer is option C.
L1 = 0.5 H (inductance of coil 1)
L2 = 4.0 H (inductance of coil 2)
k = 0.8 (coefficient of coupling)
i1 = 20 sin 314t A (current through coil 1)
To find:
Maximum value of the induced EMF in coil 2.
Formula:
The mutual inductance (M) between two coils is given by:
M = k * sqrt(L1 * L2)
The induced EMF in the second coil is given by:
e2 = -M * di1/dt
where di1/dt is the rate of change of current through coil 1.
Calculation:
Using the formula for mutual inductance, we can calculate the value of M as follows:
M = k * sqrt(L1 * L2)
= 0.8 * sqrt(0.5 * 4.0)
= 0.8 * sqrt(2.0)
≈ 0.8 * 1.414
≈ 1.131 H
Since the current through coil 1 is given by i1 = 20 sin 314t A, we can calculate the rate of change of current as follows:
di1/dt = d/dt (20 sin 314t)
= 20 * d/dt (sin 314t)
= 20 * 314 * cos 314t A/s
The maximum value of cos 314t is 1, so we can substitute this value to calculate the maximum rate of change of current:
di1/dt = 20 * 314 * 1
= 6280 A/s
Finally, we can calculate the maximum value of the induced EMF in coil 2 using the formula:
e2 = -M * di1/dt
= -1.131 * 6280 V
≈ -7091.48 V
The negative sign indicates that the induced EMF in coil 2 is in the opposite direction to the change in current in coil 1.
Since the maximum value of the induced EMF is given as a positive value, we take the absolute value:
|e2| ≈ 7091.48 V
Therefore, the maximum value of the induced EMF in coil 2 is approximately 7.1 kV (kilovolts). Hence, the correct answer is option C.
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Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. Can you explain this answer?
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Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. 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 Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. 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 Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. Can you explain this answer?.
Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. 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 Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. 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 Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Two coupled coils with L1= 0.5 H and L2= 4.0 H have a co-efficient of coupling 0.8. Find maximum value of the inductance EMF in the coil 2 if a current of i1= 20 sin 314t A is passed in coil 1.a)22.6 Vb)444 Vc)7.1 kVd)355 VCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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