Capacitor Discharge Equation How To Set Up

The short answer is that it will be as accurate as you know the value of the resistor; if you use a 5 resistor, youll be able to measure C to 5.

This blog is a collection of notes as I learn to use this microprocessor in a scientific laboratory venue and geared specifically to developing science instruments.

This tutorial will go through one way that we can combine the ComparatorA and TimerA peripherals.

In the next post, well use this combination to build a capacitance meter.

Background Capacitors are one of the three fundamental, passive components that are used in nearly every electronic device out there.

When a voltage is applied to a capacitor, it will store a charge proportional to the applied voltage.

These factors are all connected by the simple relationship Q C V.

Q is the charge, C the capacitance, and V the voltage.) When the applied voltage is removed, the charge doesnt disappear immediately, but rather decays gradually by running a current through whatever resistance is present between the capacitors two leads.

Equivalently, you can use t in s and C in F, or t in ms, R in k, and C in F.

These are more useful in formulating the calculation portion of the instrument.

Right when we disconnect the charging voltage V, the voltage across the capacitor is still V because no charge has moved yet.

In that first moment, a little chunk of charge will flow as a current through the resistance, according to the well-known Ohms Law: V I R.

Again, V is the voltage, I is the current, and R is the resistance.) After that first moment, how much charge will move in the next moment A simple picture would be to guess that the same amount will move, however thats not what happens.

Since a little charge has already left the capacitor (Q is now smaller), the voltage across it now must be a little smaller too Since we have a slightly lower voltage, the next moment will have a little less current.

The following moment a little less still, and the next a little less, and so on.

This picture describes not a linear drop in the voltage, but rather an exponential change.

If you watch the voltage on the capacitor carefully (with an oscilloscope or some other device) youll see that this is exactly what happens.

While its not a linear change, its still a simple description, and we can exploit this characteristic to find the value of the capacitance, C.

Assuming we know the resistance, all we need is to apply a voltage and time how long it takes for the voltage to decay to another known value.

Formulating the Capacitance Meter The idea behind the instrument we are going to build is simple: we charge up a capacitor, then start the timer at the moment we start discharging.

We stop the timer when the capacitor has discharged to a known point, then plug in the values into the formula.

When we invert the Discharging Capacitor Equation, we find that our measured value of C depends on the time for discharge, the resistance, and the fraction of the starting voltage to the ending voltage.

We can use ComparatorA to trigger the timer when we reach our chosen reference.

For this tutorial, well discharge the capacitor until it reaches 14 Vcc, so that we use f 4.

Capacitor Discharge Equation How To Set Up

In the next tutorial, Ill show you how to set up the peripherals and suggest a few ways that you can read the obtained result with the MSP430.