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Why is the -3dB cut-off frequency for a resistor-capacitor combination 1/RC rad/s?

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Why is the -3dB cut-off frequency for a resistor-capacitor combination 1/RC rad/s?

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This kind of problem crops up in op-amp circuits and transistor circuits, whenever a single resistor and capacitor form a potential divider and create a first-order filter. Calculation of the cut-off frequency requires the formulation of a potential divider equation.

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