A capacitive sensor has $C_x=(1000x)$ pF and is excited by $10\sin(100\pi t)$ V. It drives a high-input-impedance amplifier through a grounded shielded cable having capacitance 100 pF, as shown. At x = 0.1, find the amplifier-input voltage peak in volts.
At x = 0.1, sensor capacitance is $C_x=100$ pF. The grounded cable capacitance is 100 pF in series with the sensor as a capacitive divider, while amplifier input draws negligible current. The output fraction is $C_x/(C_x+C_c)=100/200=1/2$. Therefore its peak is $10/2=5$ V; the common angular-frequency factor cancels.
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