Sensitivity of the global electric circuit (GEC) to variations of atmospheric conductivity and current sources is analyzed and discussed. When the undisturbed exponential conductivity profile is assumed all over the Earth, the most substantial changes in the ionospheric potential (IP) are caused by conductivity perturbations inside thunderstorms; if, in addition, conductivity reduction inside thunderstorms and nonelectrified clouds is assumed, the IP becomes less sensitive to conductivity perturbations; besides, the IP is even more sensitive to source current variations than to conductivity. Current source and voltage source descriptions of GEC generators are compared; it is shown that the IP variation may critically depend on the chosen description. As an application, the IP variation due to nuclear weapons testing is studied; it is shown that neither local nor global increase of conductivity in the stratosphere could alone explain the observed 40% IP increase in the 1960s; at the same time this increase might be accounted for by a 40% increase in the source current density or a 46% reduction of the conductivity inside thunderstorms, provided that it was not reduced initially. The IP variation due to solar activity and, in particular, due to solar modulation of galactic cosmic ray flux is also discussed and modeled, which required an adequate parameterization of the rate of atmospheric ion pair production over the solar cycle. It is estimated that the maximum IP variation on the scale of the solar cycle does not exceed 5% of the mean value, unless source current perturbations are taken into account.