= RC low-pass laboratory
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The University of Colorado Boulder's Lab 3: Filters, §§7.1–7.4, specifies measuring the <resistor> and <capacitor>, then driving the assembled <RC low-pass filter> with a <function generator>. A two-channel <oscilloscope> reads actual <input> and <output> using high <electrical impedance>. Sweep the <frequency>, record the voltage <amplitude> ratio, and locate $1/\sqrt2$. A control compares a cable with a $10\times$ <oscilloscope probe> on a resistive <voltage divider>, isolating measurement <capacitance> before using the probe for the filter. A slow <square wave> then lets discharge timing estimate the <time constant> independently. Agreement supports the <RC low-pass frequency response>; source <output impedance>, probe loading, and instrument <signal bandwidth> limit it. These are prescribed measurements, with no measured dataset supplied here.<Lab 3: Filters by University of Colorado Boulder, Physics Undergraduate Labs>[Lab 3: Filters, §§7.1.1–7.1.3, Fig. 9 and §7.2.1, §§7.2.3, 7.3 and 7.4: component preparation, two-channel setup, probe control, frequency sweep and discharge timing]{ref}
The two-channel setup can also test the predicted <phase difference> directly: for positive <frequency> $f$, measure the output's time lag $\Delta t$ between corresponding features of the two <sinusoids>. For this single-stage model the phase lies between $-\pi/2$ and $0$, so choose the lag within a quarter cycle and calculate $\phi=-2\pi f\Delta t$. At the <cutoff frequency> the predicted lag is one eighth of a cycle. This tests the timing part of the <frequency response> as well as the voltage ratio.
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