Question

Two coils having self-inductance of L₁ and L₂, respectively, are magnetically coupled. The maximum possible value of mutual inductance between the coils is
1. \(\sqrt{L_1\times L_2}\)
2. L₁ + L₂
3. L₁ ÷ L₂
4. L₁ × L₂

Answer 1

Correct Answer - Option 1 : \(\sqrt{L_1\times L_2}\)

Concept:

• The inductor is an electrical component that is capable of storing electrical energy in the form of magnetic energy. 
•  The property of an electrical component that causes an emf to be generated by changing the current flow is known as inductance. Inductance is of two types
• Self-inductance: This is the phenomena in which change in electric current produce an electromotive force in the same circuit, and is given by

ϕ = L I 

Where ϕ  = Magnetic flux, L = Self inductance, I = Current

Mutual inductance: This is the phenomena in which change in flux linked with one circuit produce an emf in another coil and is given by

ϕ = MI

Where M = mutual inductance, ϕ  = magnetic flux, I = Current

The coupling coefficient is the ratio of mutual inductance to the maximum possible value of mutual inductance and is given by

\(K = \dfrac{M}{\sqrt{L_{1}L_{2}}}\)

Where M = Mutual inductance, L1, L2 = Self-inductance of coil 1 and coil 2 respectively

Explanation:

The maximum possible value of mutual inductance is at K = 1

M = \(\sqrt{L_1\times L_2}\)