  Low-frequency susceptibility of the split Cooper-pair box (SCPB) is
investigated for use in sensitive measurements of external phase or charge.
Depending on the coupling scheme, the box appears as either inductive or
capacitive reactance which depends on external phase and charge. While coupling
to the source-drain phase, we review how the SCPB looks like a tunable
inductance, which property we used to build a novel radio-frequency
electrometer. In the dual mode of operation, that is, while observed at the
gate input, the SCPB looks like a capacitance. We concentrate on discussing the
latter scheme, and we show how to do studies of fast phase fluctuations at a
sensitivity of 1 mrad/$\sqrt{Hz}$ by measuring the input capacitance of the
box.
