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# RC natural response - example

An example of the exponential natural response of an RC circuit, with real component values. Created by Willy McAllister.

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• according to the relation i(t) = v(t)/ R .. when t equals zero,
the value of i(t) will be 2V/1000 so will be 2 mA . why have you made it 1.8 ? • In the graph for current, why aren't the values for the current negative if, in a capacitor, i = C dv/dt? Since the voltage is decreasing with time, then i should be less than zero, correct? • Jamil - You make a good point. I forgot to copy the current arrow from the previous video onto the schematic in this video. The current arrow points to the left, into the top of the resistor. This means i is defined to flow up out of the capacitor (the opposite of the sign convention for passive components). This introduces a minus sign in the capacitor i-v equation. The capacitor equation is i = -C dv/dt, (with a minus sign). And that's why the current plot shows a positive spike. Thanks for pointing this out.
• So the capacitor will never get empty! • If the math is a perfect model of the RC, then you are right, the exponential never reaches 0V unless you wait infinity time. However, it's important to remember the math is a model. It models two ideal components, R and C. The model does not take into account the real world of making R's and C's. It doesn't account for how these components are made of atoms, or how the atoms are vibrating due to the temperature. So in reality, the model has limitations. In the real world, the charge on the capacitor gets so low you can't tell it apart from normal electron activity at room temperature. After 5 or 10 time constants, for all practical purposes the charge on the capacitor is zero.
• This equation implies that the capacitor never discharged completely nor the current falls to zero... Is this phenomenon real? • Good question. If you look at the mathematical equation you know that the exponential term never actually goes to zero. The thing to remember is that these equations are models of the real-world circuits we build. And those models are really useful but they are incomplete, and don't capture absolutely everything about a real capacitor and real resistor. Like for example the model knows nothing about temperature and vibrating atoms and Brownian motion. So from a practical engineering point of view, if time is allowed to go out for 5 or 10 times the value of RC, we recognize that the RC response is pretty much over. The voltage gets very very small and "sinks into the noise," becoming indistinguishable from 0 volts. 