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My textbook states that the inductance of an inductor depends only on the geometry of the inductor. Moreover, the formulas used to calculate self-inductance and mutual inductance are the same. So, is the inductance of an inductor calculated from mutual inductance and self-inductance the same or are they different?

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Moreover, the formulas used to calculate self-inductance and mutual inductance are the same.

This does not sound right. Self-inductance is due to induced electric field of the coil acting back on the current in that same coil. Mutual inductance is due to induced electric field of one coil acting on current in the other coil.

So, is the inductance of an inductor calculated from mutual inductance and self-inductance the same or are they different?

They are different concepts, and usually have different value. Mutual inductance depends on geometry of both coils. Self-inductance depends on geometry of single coil.

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