**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

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### 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)