Combination of Inductance
Category : JEE Main & Advanced
(1) Series : If two coils of self-inductances \[{{L}_{1}}\] and \[{{L}_{2}}\] having mutual inductance are in series and are far from each other, so that the mutual induction between them is negligible, then net self inductance \[{{L}_{S}}={{L}_{1}}+{{L}_{2}}\]
When they are situated close to each other, then net inductance \[{{L}_{S}}={{L}_{1}}+{{L}_{2}}\pm 2M\]
(2) Parallel : If two coils of self-inductances \[{{L}_{1}}\] and \[{{L}_{2}}\] having mutual inductance are connected in parallel and are far from each other, then net inductance \[L\] is \[\frac{1}{{{L}_{P}}}=\frac{1}{{{L}_{1}}}+\frac{1}{{{L}_{2}}}\] \[\Rightarrow \]\[{{L}_{P}}=\frac{{{L}_{1}}{{L}_{2}}}{{{L}_{1}}+{{L}_{2}}}\]
When they are situated close to each other, then
\[{{L}_{P}}=\frac{{{L}_{1}}{{L}_{2}}-{{M}^{2}}}{{{L}_{1}}+{{L}_{2}}\pm 2M}\]
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