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It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately 36.8% of its initial charge voltage.
This time constant determines the charge/discharge time. A 100 F capacitor with an internal resistance of 30 mΩ for example, has a time constant of 0.03 • 100 = 3 s. After 3 seconds charging with a current limited only by internal resistance, the capacitor has 63.2% of full charge (or is discharged to 36.8% of full charge).
This is in keeping with the intuitive point that the capacitor will be charging from the supply voltage as time passes, and will eventually be fully charged. These equations show that a series RC circuit has a time constant , usually denoted τ = RC being the time it takes the voltage across the component to either rise (across the capacitor ...
A discharged or partially charged capacitor appears as a short circuit to the source when the source voltage is higher than the potential of the capacitor. A fully discharged capacitor will take approximately 5 RC time periods to fully charge; during the charging period, instantaneous current can exceed steady-state current by a substantial ...
In the short-time limit, if the capacitor starts with a certain voltage V, since the voltage drop on the capacitor is known at this instant, we can replace it with an ideal voltage source of voltage V. Specifically, if V=0 (capacitor is uncharged), the short-time equivalence of a capacitor is a short circuit.
This charges or discharges the capacitor over time. Because the resistor and capacitor are connected to a virtual ground, the input current does not vary with capacitor charge, so a linear integration that works across all frequencies is achieved (unlike RC circuit § Integrator ).
The total electrostatic potential energy stored in a capacitor is given by = = = where C is the capacitance, V is the electric potential difference, and Q the charge stored in the capacitor. Outline of proof
When S 2 is closed (S 1 is open - they are never both closed at the same time), some of that charge is transferred out of the capacitor. Exactly how much charge gets transferred can't be determined without knowing what load is attached to the output. However, by definition, the charge remaining on capacitor can be expressed in terms of the ...