If I'm not mistaken, you can determine the capacitance of a capacitor using just a voltage source, a resistor, and the scope to check the time it takes to charge the cap to a specific voltage. Don't remember the formula, but "time constant calculator" and "capacitor" together may give you the answers for that in google.
ESR is a bit more difficult, as it requires a signal generator.
See attached which shows a capacitor charging (10k 0.1 ufd -> 1 time constant is 1 ms). Note how close to 1ms the voltage reaches about 63%. I can play with this resistor/capacitor circuit all day!
Measurements are taken from rising edge of the square wave.
There's an explanation of capacitor charging here:
https://www.electronics-tutorials.ws/rc/rc_1.htmlBasically, you want to know when the capacitor voltage is 63% of the applied voltage as this occurs at 1 time constant. Given a measured time to get to 63% and a given resistor, you can work backwards to get C.
Vout = Vsource * (1 - e
-t/RC) R is in Ohms, C is in Farads, t is in seconds
The product RC is sometimes called Tau - the time constant. You want to adjust the resistor to get t / Tau = 1. Once you do, simply solve for C from t / Tau = 1 and Tau = RC so t / RC = 1. For my example above t = 1 ms, R = 10k and C = 0.1 ufd (but we're going to calculate the value) so:
10
-3 / (10
4 * C) = 1 so C = 10
-3 / 10
4 or 10
-7 Farads or 0.1 ufd. Just what we expected.
To clear up any confusion on scientific notation:
10
-3 is 1 ms
10
4 is 10k
10
-7 is 0.1 ufd
I use this because I learned the subject using a slide rule and I do most of the math in my head. It's easier when using scientific notation.