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A method to extract the equivalent parameters of transient electric circuit and magnetic field coupled problem based on sensitivity computation on the system equations is presented. The field equations are derived by using the finite element method. In contrast to traditionally used methods which are based on the physical meanings and physical relationships of the parameters, in this method, the parameters are extracted from the mathematical system equations which include the eddy-current magnetic field equations and internal circuit equations. Its advantage is that it is applicable to complex problems, inside which the reactive energy, iron losses, and copper losses are difficult to be isolated and expressed. The extracted parameters can include the effects of eddy currents, internal circuits, and mechanical motion. It has been applied to indirect coupling between external circuits and transient magnetic field with internally connected circuits.