A resistor–capacitor low-pass filter

Let slow changes pass

RC means Resistor Capacitor: a resistor and capacitor work together. A low-pass filter preserves slower changes and reduces faster ones. Gain here is output sine-wave amplitude divided by input amplitude; cutoff is where gain becomes about 70.7%. A nanofarad (nF) is one billionth of a farad, a unit of capacitance; a millisecond (ms) is one thousandth of a second.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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Why it works

Ideal sine-wave steady state, output measured across the capacitor, no load. A startup transient and component tolerances are not simulated.

τ = RC is the time constant. fc = 1/(2πRC) is cutoff frequency. Gain = 1/√(1 + (f/fc)²). nF means nanofarad, one billionth of a farad. Here R is resistance, C is capacitance, and f is the input signal frequency.

Difficulty

Build · Build it
Power on with 10 kΩ, 100 nF and a 100 Hz signal. Observe gain near 84.67%.
Need a hint?
10 kΩ; 100 nF; 100 Hz → 84.67%
Explore · Change one thing
At 1000 Hz, obtain gain at most 20% with a time constant at most 2 ms.
Need a hint?
10 kΩ; 100 nF; 1000 Hz → 15.72%
Solve it · Solve the challenge
At 160 Hz, obtain cutoff 150–170 Hz and gain 68–73%.
Need a hint?
10 kΩ; 100 nF; 160 Hz → 70.52%

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