RC Circuit - Natural Response

Natural Response

The simplest RC circuit is a capacitor and a resistor in series. When a circuit consists of only a charged capacitor and a resistor, the capacitor will discharge its stored energy through the resistor. The voltage across the capacitor, which is time dependent, can be found by using Kirchhoff's current law, where the current through the capacitor must equal the current through the resistor. This results in the linear differential equation

C\frac{dV}{dt} + \frac{V}{R}=0 .

Solving this equation for V yields the formula for exponential decay:

V(t)=V_0 e^{-\frac{t}{RC}} \ ,

where V0 is the capacitor voltage at time t = 0.

The time required for the voltage to fall to is called the RC time constant and is given by

Read more about this topic:  RC Circuit

Famous quotes containing the words natural and/or response:

    “Criticism is infested with the cant of materialism, which assumes that manual skill and activity is the first merit of all men, and disparages such as say and do not, overlooking the fact, that some men, namely, poets, are natural sayers, sent into the world to the end of expression, and confounds them with those whose province is action, but who quit to imitate the sayers.”
    —Ralph Waldo Emerson (1803–1882)

    “Perhaps nothing in all my business has helped me more than faith in my fellow man. From the very first I felt confident that I could trust the great, friendly public. So I told it quite simply what I thought, what I felt, what I was trying to do. And the response was quick, sure, and immediate.”
    —Alice Foote MacDougall (1867–1945)