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If it is a variable cap, apply AC signal to the capacitor as per its specifications.This is done because the variation in the voltage gives a corresponding current output due to the charging and discharging of capacitor.

Then a Trans-impedance amplifier can be used to convert this input current to voltage. Current amplifier can be used to amplify the current at the input of the trans-impedance amplifier. Similarly a voltage amplifier can be used at the out put of the trans-impedance amplifier to amplify the voltage output.

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Q: What is the simplest way to convert capacitance to voltage?
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