Read all the "RC Circuits Transient Analysis with Raspberry Pi and Scoppy" series:
- 1 - Introduction
- 2 - Building the Circuit
- 3 - Measurements and Data Analysis
- 4 - Further Experiments
In this 4th and last episode we will explore further variants of the circuits.
Increase Time Constant \(\tau = RC\)
As we already have seen in 1 - Introduction, \(\tau = RC\) is the so-called Time Constant that tells us how quickly an RC circuit reacts to changes in voltage. To recap:
- higher \(\tau\) (= longer reaction time): the curve will evolve more slowly
- lower \(\tau\) (= shorter reaction time): the curve will evolve more quickly
When building the circuit we choose a \(C = 10 \mu F\) capacitor and a \(R = 220 \Omega\) resistor, thus our Time Constant is currently at the following nominal value:
(In Measurements and Data Analysis we actually found out that the real Time Constant is a bit bigger and at around \(2.8 ms\) but it won't matter much for today's expertiment).
We are going to double it just by increasing the capacity value adding a second \(10 \mu F\) capacitor to the circuit. As you may know, when adding capacitors in parallel the total capacity is the sum of all the parallel capacities. Thus, we expect:
The exact number does not matter as we're not going to precisely measure the curve, but at least we have an idea of what to expect: a slower curve, roughly the same order of magnitude of the original \(\tau = 2.2 ms\) one but just a bit slower (remember that \(\tau\) is an exponent).
In the pictures below you can see the two different configurations:
- Configuration A: original \(10 \mu F\) capacitor configuration
- Configuration B: \(20 \mu F\) variant
Check out how the capacitors are mounted in parallel and how the increased capacity changes the shape of the curve:
Configuration A
Configuration B
Variable resistance
In this variant we will change te resistance instead of the capacity, but in a lot more fun way: we will use a rotative potentiometer!
A common place where you can find such type of circuit is an electric guitar: the tone contol is exactly this: a variable-resistance RC circuit. When the pot is closed, i.e. when is rotated completely counter-clockwise, the high frequencies are cut, while the low frequencies pass unchanged; when the pot is open, the signal passes almost unchanged. The trick here is to think about high frequencies a fast-transient signals, and when you measure the voltage across a RC circuit you find out that it acts on those specifically.
Turning the knob changes the \(\tau\) from an almost-perfect square wave to a "shark's fin" figure:
You can see the circuit and oscilloscope in action in this clip I posted on YouTube: