**DC Circuits**

A series circuit containing only a resistor, a capacitor, a switch and a constant DC source of voltage * V_{0}* is known as a

*charging circuit*. If the capacitor is initially uncharged while the switch is open, and the switch is closed at

*= 0, it follows from Kirchhoff's voltage law that*

**t**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

*. The initial current is then*

**V**_{0}*(0) =*

**i***/*

**V**_{0}*. With this assumption, the differential equation yields*

**R**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 * V_{0}* and the final voltage being zero.

Read more about this topic: Capacitor, Theory of Operation

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

**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 ...

... 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 ...

... 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)