Question

Coefficients of coupling between two coils of self-inductances $ {{L}_{1}} $ and $ {{L}_{1}} $ is unity. It means:

• A. $50\%$ flux of $ {{L}_{1}} $ is linked with $ {{L}_{2}} $
• B. $100\%$ flux of $ {{L}_{1}} $ is linked with $ {{L}_{2}} $
• C. $ \sqrt{{{L}_{1}}} $ time of flux $ {{L}_{1}} $ is linked with $ {{L}_{2}} $
• D. None of above

Answer 1

Answer: (B)

Two coils are said to be magnetically coupled, if full or a part of the flux produced by one links with the other. Let $L_{1}$ and $L_{2}$ be the self-inductances of the coils and $M$ be their mutual inductances, then
$k=\frac{M}{\sqrt{L_{1} L_{2}}}$
When $100 \%$ flux produced by one coil links with the other, then mutual inductance between the two is maximum and is given by
$M=\sqrt{L_{1} L_{2}}$
In that case, $k=1$ (unity)
Note: When there is no common flux between the two coils, they are said to be magnetically isolated. In this case, $k = C$ and $M =0 .$ In practice $k$ lies between $O$ and $1 .$