Two coils are wound separately on identical ring-shaped ferromagnetic cores. Coil 1 has N turns and wire gauge G, while coil 2 has 2N turns and gauge G/2. Find self-inductance ratio L₂/L₁.
For identical core geometry and permeability, inductance is proportional to the square of the number of turns: L=μN²A/ℓ. Doubling turns therefore multiplies self-inductance by four. Wire gauge affects resistance and packing but not this ideal core-inductance ratio. Thus L₂/L₁=4.
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