# Basic Electrical Engineering Questions and Answers – Coupling Coefficient

This set of Basic Electrical Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Coupling Coefficient”.

1. What is the coupling coefficient when all the flux of coil 1 links with coil 2?
a) 0
b) 100
c) 1
d) Insufficient information provided

Explanation: When all the flux of coil 1 links with coil 2 it is known as an ideal coupling where the coupling coefficient is 1.

2. What is the coupling coefficient when there is ideal coupling?
a) 0
b) 100
c) 1
d) Insufficient information provided

Explanation: When all the flux of coil 1 links with coil 2 it is known as an ideal coupling where the coupling coefficient is 1.

3. Can the coupling coefficient practically ever be equal to 1?
a) Yes
b) No
c) Depends on the current in coil 1
d) Depends on the current in coil 2

Explanation: All the flux of coil 1 can never link with coil 2. Loss occurs practically due to which coupling coefficient cannot be equal to 1.

4. Mutual inductance between two coupled coils depend on?
b) Rate of change of flux linkage
c) Rate of change of current
d) Flux density

Explanation: Faraday’s law of induction states that the magnitude of the induced EMF is the product of the number of turns of the coil and the rate of change of flux linkage in it. Hence, the mutual inductance depends on the rate of change of flux linkage.

5. Which, among the following, is the correct formula to find the coupling coefficient?
a) k=M/sqrt(L1L2)
b) k=M/sqrt(L12)
c) k=M/sqrt(L22)
d) k=M/(L1L2)

Explanation: The correct formula for the coupling coefficient is k=M/sqrt(L1L2). Where L1 and L2 are the inductance values of the first and second coil respectively and M is the mutual inductance.
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6. What happens to the coupling coefficient when the flux linkage of coil 1 and coil 2 increases?
a) Increases
b) Decreases
c) Remains the same
d) Becomes zero

Explanation: When the flux linkage of coil 1 and coil 2 increases, its mutual inductance increases. The coupling coefficient is directly proportional to the mutual inductance hence as mutual inductance increases, the coupling coefficient increases.

7. What is the SI unit of coupling coefficient?
a) H
b) H-1
c) No unit
d) H2

Explanation: The expression to find mutual inductance is k=M/sqrt(L1L2)= H/sqrt(H*H)= 1. Therefore it does not have any unit.

8. Find the coupling coefficient if the Mutual inductance is 20H, the inductance of coil 1 is 2H and the inductance of coil 2 is 8H.
a) 5
b) 20
c) 2
d) 8

Explanation: we know that:
k=M/sqrt(L1L2)
Substituting the values from the question, we get k=5.

9. Find the value of x if the Mutual inductance is x H, the inductance of coil 1 is 2H and the inductance of coil 2 is 8H. The coupling coefficient is 5.
a) 10H
b) 20H
c) 16H
d) 15H

Explanation: we know that:
k=M/sqrt(L1L2)
Substituting the values from the question, we get M=20H.

10. Find the value of x if the Mutual inductance is 20H, the inductance of coil 1 is xH and the inductance of coil 2 is 8H. The coupling coefficient is 5.
a) 2H
b) 4H
c) 6H
d) 8H

Explanation: we know that:
k=M/sqrt(L1L2)
Substituting the values from the question, we get L1=2H.

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