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A mathematical analysis of a parallel‐connected magnetic amplifier with a resistive load is presented. The analysis is based on two distinct analytical approximations of the magnetization curve of the core material; a polynomial and a hyperbolic function. The variation of the core flux and the output current of the amplifier as a function of time are determined by the solution of an integral equation. A finite difference method is developed to determine the response of the loaded amplifier that makes direct use of the magnetization curve of the core material.