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Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.
The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______
The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______
- a)3.14 cos (314t) V
- b)3.33 sin (314t) V
- c)6.66 cos (314t) V
- d)6.28 cos (314t) V
Correct answer is option 'C'. Can you explain this answer?
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Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The ...
Given data:
L1 = 10 mH (self-inductance of coil 1)
L2 = 20 mH (self-inductance of coil 2)
K = 0.75 (coefficient of coupling)
We need to find the voltage in the second coil when the current in the circuit is given by I = 2 sin (314t) A.
To solve this problem, we can use the concept of mutual inductance and the formula for calculating the voltage induced in a coil due to mutual inductance.
Mutual Inductance:
Mutual inductance is a measure of the extent to which a change in current in one coil induces an electromotive force (EMF) in another coil. It is denoted by M.
Formula for Voltage Induced:
The voltage induced in a coil due to mutual inductance is given by the formula:
V2 = -M dI1/dt
Where:
V2 is the voltage induced in the second coil,
M is the mutual inductance between the two coils,
dI1/dt is the rate of change of current in the first coil.
Calculating Mutual Inductance:
The mutual inductance between two coils can be calculated using the formula:
M = K sqrt(L1 * L2)
Where:
K is the coefficient of coupling,
L1 and L2 are the self-inductances of the two coils.
Substituting the given values:
L1 = 10 mH = 10 * 10^-3 H
L2 = 20 mH = 20 * 10^-3 H
K = 0.75
M = 0.75 * sqrt(10 * 10^-3 * 20 * 10^-3) = 0.75 * sqrt(200 * 10^-6) = 0.75 * 0.014142 = 0.010606
Calculating Rate of Change of Current:
Given current I = 2 sin (314t) A
The rate of change of current can be calculated by taking the derivative of I with respect to time (t):
dI1/dt = 2 * 314 cos (314t)
Substituting the values into the formula:
V2 = -M dI1/dt
= -0.010606 * 2 * 314 cos (314t)
= -6.66 cos (314t) V
Therefore, the voltage in the second coil when the current in the circuit is given by I = 2 sin (314t) A is 6.66 cos (314t) V. Hence, option C is the correct answer.
L1 = 10 mH (self-inductance of coil 1)
L2 = 20 mH (self-inductance of coil 2)
K = 0.75 (coefficient of coupling)
We need to find the voltage in the second coil when the current in the circuit is given by I = 2 sin (314t) A.
To solve this problem, we can use the concept of mutual inductance and the formula for calculating the voltage induced in a coil due to mutual inductance.
Mutual Inductance:
Mutual inductance is a measure of the extent to which a change in current in one coil induces an electromotive force (EMF) in another coil. It is denoted by M.
Formula for Voltage Induced:
The voltage induced in a coil due to mutual inductance is given by the formula:
V2 = -M dI1/dt
Where:
V2 is the voltage induced in the second coil,
M is the mutual inductance between the two coils,
dI1/dt is the rate of change of current in the first coil.
Calculating Mutual Inductance:
The mutual inductance between two coils can be calculated using the formula:
M = K sqrt(L1 * L2)
Where:
K is the coefficient of coupling,
L1 and L2 are the self-inductances of the two coils.
Substituting the given values:
L1 = 10 mH = 10 * 10^-3 H
L2 = 20 mH = 20 * 10^-3 H
K = 0.75
M = 0.75 * sqrt(10 * 10^-3 * 20 * 10^-3) = 0.75 * sqrt(200 * 10^-6) = 0.75 * 0.014142 = 0.010606
Calculating Rate of Change of Current:
Given current I = 2 sin (314t) A
The rate of change of current can be calculated by taking the derivative of I with respect to time (t):
dI1/dt = 2 * 314 cos (314t)
Substituting the values into the formula:
V2 = -M dI1/dt
= -0.010606 * 2 * 314 cos (314t)
= -6.66 cos (314t) V
Therefore, the voltage in the second coil when the current in the circuit is given by I = 2 sin (314t) A is 6.66 cos (314t) V. Hence, option C is the correct answer.
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Community Answer
Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The ...
M=k√wl^2
m=0.75√200
=10.68
=0.1068 H
v2= m di/dt
=0.106 d/dt (2sin(314t)
6.66cos(314t) v
m=0.75√200
=10.68
=0.1068 H
v2= m di/dt
=0.106 d/dt (2sin(314t)
6.66cos(314t) v
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Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer?
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Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) 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 have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) 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 have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer?.
Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) 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 have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) 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 have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) 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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Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two coupled coils have self inductances L1 = 10 mH and L2 = 20 mH.The co-efficient of coupling (K) being 0.75 in the air. Voltage in the second coil when the current in circuit is given by I = 2 sin (314t) A is _______a)3.14 cos (314t) Vb)3.33 sin (314t) Vc)6.66 cos (314t) Vd)6.28 cos (314t) VCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
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