A) \[M={{L}_{1}}{{L}_{2}}\]
B) \[M={{L}_{1}}/{{L}_{2}}\]
C) \[M=\sqrt{{{L}_{1}}{{L}_{2}}}\]
D) \[M={{({{L}_{1}}{{L}_{2}})}^{2}}\]
Correct Answer: C
Solution :
\[M=-\frac{{{e}_{2}}}{d{{i}_{1}}/dt}=-\frac{{{e}_{1}}}{d{{i}_{2}}/dt}\] Also \[{{e}_{1}}=-{{L}_{1}}\frac{d{{i}_{1}}}{dt}.{{e}_{2}}=-{{L}_{2}}\frac{d{{i}_{2}}}{dt}\] \[{{M}^{2}}=\frac{{{e}_{1}}{{e}_{2}}}{\left( \frac{d{{i}_{1}}}{dt} \right)\ \left( \frac{d{{i}_{2}}}{dt} \right)}={{L}_{1}}{{L}_{2}}\Rightarrow M=\sqrt{{{L}_{1}}{{L}_{2}}}\]
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