Grab a 15 kOhm resistor and a 0.01 ufd capacitor and wire them in series with the other side of the capacitor connected to ground. Insert a 1 kHz sine wave of some amplitude, say 1V, into the resistor (between the resistor and ground). Connect Ch1 probe between the input and ground. Connect Ch2 probe between the junction of the resistor/capacitor and ground. Get things displaying on the screen and prove (using cursors and math) that the phase shift is very nearly 45 degrees. Hint: Using properly placed cursors Bx-Ax about 125 us. Why is that 45 degrees? Note that 45 degrees is 1/8 of a cycle and 125 is 1/8 of 1 ms (1 kHz). Calculate the capacitive reactance, draw the impedance vector diagram and calculate the theoretical phase shift. What frequency gets exactly 45 degrees (measured and theoretical)?
http://keisan.casio.com/exec/system/1258032632Same circuit, insert frequencies like 10 Hz, 100 Hz, 1000 Hz, 10,000 Hz and record capacitor voltage. Determine -3 dB point for low pass filter. You can use a DMM or get the values from your scope. -3dB occurs when voltage at some higher frequency (like 1kHz) is 0.707 of applied voltage.
http://www.learningaboutelectronics.com/Articles/Low-pass-filter-calculator.phphttp://www.aetechron.com/db_to_Voltage_Calculator_home.shtmlThere's a reason that the -3dB point (corner frequency) turns out to have a 45 degree phase shift.
http://www.electronics-tutorials.ws/filter/filter_2.html See the phase shift diagrams at "Frequency Response of..."
Same circuit, insert 500 Hz square wave and watch the rising and falling edges. Calculate Tau (RC time constant) and prove that you have more than 6 Tau for both edges. If you do have more than 6 Tau, what percent of the input voltage is stored on the capacitor after 6 Tau. How high is the voltage in 1 Tau, 2, 3, 4 and 5 as a percentage. Hint: voltage in 1 Tau is about 63%
http://mustcalculate.com/electronics/rctimeconstant.php?c=0.01u&r=15000 gives 150 microseconds.
150 microseconds times 6 gives about 1 millisecond so we allow 1 ms for charge and 1 ms for discharge, hence 500 Hz.
There's a bunch to learn with a simple resistor and capacitor. Turns out I was building up these very experiments to show my grandson. He is considering EE as his major.
You can make up the same sequence of experiments for an inductor. Just pick a value that matches some resistor value and center frequency:
http://www.learningaboutelectronics.com/Articles/Low-pass-filter-calculator.php#answer2The resistance of the inductor may not be insignificant. You can include it as a resistor in series with the real resistor.