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Mercury lacks an (significant) ionosphere, leading to the hypothesis that its large-scale field-aligned currents (FACs) are instead closed through its highly conductive core. Mercury's interior is usually characterized by a two-layer model: a resistive outer layer (the crust and mantle) and a conductive inner layer (the iron-rich core). While this model is widely used, the effects of Mercury's conductivity and core on FACs have not been extensively explored. Therefore, we conducted analytical calculations combined with hybrid-kinetic simulations to study these effects. We found that the total currents of FACs are enhanced by ∼2 times when a conducting core is included, and the current density is directly proportional to the outer layer's conductivity. Combining our analysis with previous observations, the conductivity of the outer layer is estimated to be ∼5.4×10−7−1.1×10−6S/m. Our study suggests that future observations of Mercury's FACs will better constrain Mercury's conductivity profile.