  We present a sensitive, tunable radio-frequency resonator designed to detect
reactive changes in nanoelectronic devices down to dilution refrigerator
temperatures. The resonator incorporates GaAs varicap diodes to allow
electrical tuning of the resonant frequency and the coupling to the input line.
We find a resonant frequency tuning range of 8.4 MHz at 55 mK that increases to
29 MHz at 1.5 K. To assess the impact on performance of different tuning
conditions, we connect a quantum dot in a silicon nanowire field-effect
transistor to the resonator, and measure changes in the device capacitance
caused by cyclic electron tunneling. At 250 mK, we obtain an equivalent charge
sensitivity of $43~\mu e / \sqrt{\text{Hz}}$ when the resonator and the line
are impedance-matched and show that this sensitivity can be further improved to
$31~\mu e / \sqrt{\text{Hz}}$ by re-tuning the resonator. We understand this
improvement by using an equivalent circuit model and demonstrate that for
maximum sensitivity to capacitance changes, in addition to impedance matching,
a high-quality resonator with low parasitic capacitance is desired.
