  What is the complex impedance of a fully coherent quantum
resistance-capacitance (RC) circuit at GHz frequencies in which a resistor and
a capacitor are connected in series? While Kirchhoff's laws predict addition of
capacitor and resistor impedances, we report on observation of a different
behavior. The resistance, here associated with charge relaxation, differs from
the usual transport resistance given by the Landauer formula. In particular,
for a single mode conductor, the charge relaxation resistance is half the
resistance quantum, regardless of the transmission of the mode. The new
mesoscopic effect reported here is relevant for the dynamical regime of all
quantum devices.
