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When 2 inductors share the same magnetic field they become coupled and besides their self inductance they have a mutual inductance as well.
For this circuit:
![](https://electrical.codidact.com/uploads/9BbSeaQgDrCoxDMhzybYnxP9)
Now current entering one coil marked with a dot , produces a current exitting the couple coil at its dotting end.In L1 current enters from the dotted end so this creates a current which exits from the dotted end of L2 and in L2 current enters from the dotted end so this again creates a current which exits from the dotted end of L1 so we get 2 voltage drops from self inductance of each coil and 2 voltage drops from the mutual inductance of the coupled coils.
![I](https://electrical.codidact.com/uploads/9rF1TGmSbyjXheyYbaf81p3z)
so that is translated to this equation:
![](https://electrical.codidact.com/uploads/emSsaAC41ngoDAQM1JsoPyNq)
Now obviously :
![](https://electrical.codidact.com/uploads/UGnT3PZrtT6aqkMHLrsnwmdq)
The total inductance of the circuit becomes ![](https://electrical.codidact.com/uploads/vdsK3wj6wSQYEpeKCPvXCnpv)
~~the value of the mutual inductance is:(with k=1)~~
![](https://electrical.codidact.com/uploads/X3znhTfjLipcUBHdWcQUfpv4)
~~$L_{T}=4H$~~
and the equation of current of this circuit becomes
![](https://electrical.codidact.com/uploads/6q6XKefrqD8ZUzYHqmJNcKox)

When 2 inductors share the same magnetic field they become coupled and besides their self inductance they have a mutual inductance as well.
For this circuit:
![](https://electrical.codidact.com/uploads/9BbSeaQgDrCoxDMhzybYnxP9)
Now current entering one coil marked with a dot, produces a current exiting the couple coil at its dotting end. In L1 current enters from the dotted end so this creates a current which exits from the dotted end of L2 and in L2 current enters from the dotted end so this again creates a current which exits from the dotted end of L1 so we get 2 voltage drops from self inductance of each coil and 2 voltage drops from the mutual inductance of the coupled coils.
![I](https://electrical.codidact.com/uploads/9rF1TGmSbyjXheyYbaf81p3z)
so that is translated to this equation:
![](https://electrical.codidact.com/uploads/emSsaAC41ngoDAQM1JsoPyNq)
Now obviously :
![](https://electrical.codidact.com/uploads/UGnT3PZrtT6aqkMHLrsnwmdq)
The total inductance of the circuit becomes ![](https://electrical.codidact.com/uploads/vdsK3wj6wSQYEpeKCPvXCnpv)
the value of the mutual inductance is: (with k=1)
![](https://electrical.codidact.com/uploads/X3znhTfjLipcUBHdWcQUfpv4)
$L_{T}=4 \text{H}$
and the equation of current of this circuit becomes
![](https://electrical.codidact.com/uploads/6q6XKefrqD8ZUzYHqmJNcKox)