  In circuits containing closed loops the operator for the current is
determined by charge conservation up to an arbitrary divergenceless current. In
this work we propose a formula to calculate the magnetically active circulating
current $I_{\rm ring}$ flowing along a quantum ring connected to biased leads.
By {\em gedanken experiments} we argue that $I_{\rm ring}$ can be obtained from
the response of the gran-canonical energy of the ring to an external magnetic
flux. The results agree with those of the conventional approach in the case of
isolated rings. However, for connected rings $I_{\rm ring}$ cannot be obtained
as a linear combination of bond currents.
