Electro Magnetic Induction And Alternating Currents Question 526
Question: Two coils of self-inductance $ L_{1} $ and $ L_{2} $ are placed closer to each other so that total flux in one coil is completely linked with other. If $ M $ is mutual inductance between them, then [DCE 2002]
Options:
A) $ M=L_{1}L_{2} $
B) $ M=L_{1}/L_{2} $
C) $ M=\sqrt{L_{1}L_{2}} $
D) $ M={{(L_{1}L_{2})}^{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ M=-\frac{e_{2}}{di_{1}/dt}=-\frac{e_{1}}{di_{2}/dt} $
Also $ e_{1}=-L_{1}\frac{di_{1}}{dt}.e_{2}=-L_{2}\frac{di_{2}}{dt} $ $ M^{2}=\frac{e_{1}e_{2}}{( \frac{di_{1}}{dt} )\ ( \frac{di_{2}}{dt} )}=L_{1}L_{2}\Rightarrow M=\sqrt{L_{1}L_{2}} $
