We formulate a simple model which describes the interplay between electromagnetic forces, inertia, and gravity in liquid-metal current-limiting devices utilizing the electromagnetic pinch effect. The dynamics of this system, called an H-trough, is completely described by a nonlinear ordinary differential equation for the fluid's cross-section as a function of time. A bifurcation analysis of stationary states is performed. For a wide range of geometry parameters the cross-section of the fluid is found to be a discontinuous function of the electrical current. The jump in cross-section above some critical current is accompanied by a strong increase of the total electric resistance of the system and results in the current-limiting action of the device by the pinch effect. An experimental study of the system confirms the predicted switching behaviour. For low electric current the experiment is in excellent quantitative agreement with the theory, while for high electric current three-dimensional instabilities and end effects render the agreement with the one-dimensional model less satisfactory. Our model enables us to isolate the pertinent non-dimensional parameters for liquid-metal current limiters and to derive the scaling law of the critical electric current as a function of the geometry and material properties of the system.