Who can tell me the theory about the LCR bridge to measure capacitance?
Google to the rescue: lcr bridge measure capacitance
The ac bridges work just like the wheatstone bridge except you have to balance the impedance, which is dependent upon the frequency. By taking a ratio of impedances, you can calculate the capacitance or inductance as required.
The ac bridges are pretty much obsolete in modern test equipment. Today's LCR meters work by introducing a small sinusoidal voltage to a network (capacitor, inductor, resistor or combinations), and measuring the current that flows into the circuit. By the ohm's law, the impedance can be calculated Z = V/I, from which capacitance or inducance can be deduced.
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