Ampere's circuital law relates the line integral of the magnetic field around a closed path to:
The net current enclosed by the path.
Ampere's circuital law states \(\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}\).
The line integral of B around any closed loop equals μ₀ times the net (algebraic) current passing through the surface bounded by the loop.
Resistance does not appear in the law; enclosed electric field is not part of it (circulation of E relates to changing flux in Faraday’s law); magnetic flux through a closed surface is the subject of Gauss’s law for magnetism, not Ampere’s law.
Hence, the answer is The net current enclosed by the path.
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