$\"\"$

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(1)

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Step 1:

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Find the total impedance.

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The inductive impedances are $\"\"$ , $\"\"$ and $\"\"$ .

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The mutual inductance are $\"\"$ .

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Find the total inductance at the coil 1:

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$\"\"$

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Find the total inductance at the coil 2:

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$\"\"$

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Find the total inductance at the coil 3:

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$\"\"$

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Step 2:

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Total impedance between the nodes $\"\"$ and $\"\"$ is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ is in series with $\"\"$

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$\"\"$

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$\"\"$

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Step 3:

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Find the total current in the circuit.

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$\"\"$

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$\"\"$

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$\"\"$

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Total current in the circuit is $\"\"$

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(2)

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Redraw the circuit representing the loop currents.

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$\"\"$

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Apply KVL to the loop 1:

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$\"\"$

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Apply KVL to the loop 2:

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$\"\"$

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Apply KVL to the loop 3:

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$\"\"$

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Substitute equation (1) and equation (3) in equation (2).

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$\"\"$

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