# Capacitor - Theory of Operation - DC Circuits

DC Circuits

A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage V0 is known as a charging circuit. If the capacitor is initially uncharged while the switch is open, and the switch is closed at t = 0, it follows from Kirchhoff's voltage law that

Taking the derivative and multiplying by C, gives a first-order differential equation,

At t = 0, the voltage across the capacitor is zero and the voltage across the resistor is V0. The initial current is then i (0) =V0 /R. With this assumption, the differential equation yields

where is the time constant of the system.

As the capacitor reaches equilibrium with the source voltage, the voltages across the resistor and the current through the entire circuit decay exponentially. The case of discharging a charged capacitor likewise demonstrates exponential decay, but with the initial capacitor voltage replacing V0 and the final voltage being zero.

### Other articles related to "dc circuits, circuit, dc, circuits":

Capacitator - Theory of Operation - DC Circuits
... See also RC circuit A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage V0 is known as a charging circuit ... the voltages across the resistor and the current through the entire circuit decay exponentially ...
Recreational Vehicle - Terms
... with a disconnect turned off, that battery circuit is 'dead' and no power will be available from the batteries ... The isolator also prevents power use by the circuits drawing on the house battery from also draining the engine or vehicle battery ... and converts that power to 12 volts DC for use in the vehicle ...
Capacitator - Non-ideal Behavior - Current and Voltage Reversal
... Voltage reversal is the change of polarity in a circuit ... In DC circuits this will usually be less than 100%, (often in the range of 0 to 90%), whereas AC circuits experience 100% reversal ... In DC circuits and pulsed circuits, current and voltage reversal are affected by the damping of the system ...

### Famous quotes containing the word circuits:

The Buddha, the Godhead, resides quite as comfortably in the circuits of a digital computer or the gears of a cycle transmission as he does at the top of a mountain or in the petals of a flower.
Robert M. Pirsig (b. 1928)