Tricky Circuit

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.

Open interactive experiment

EXPERIMENT BENCH

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

Sign in to save progress. Guest progress stays on this device.

Open laboratory in a full window

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
  1. 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%

  2. 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%

  3. 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%

Extra reading and circuit recipes

Let slow changes pass

A useful pattern

Doubling R or C halves the cutoff and doubles the time constant.

Beyond this model

Connecting a real load changes the network; this formula assumes no output loading.

A useful trap to avoid

Cutoff is not a wall: frequencies above it are reduced gradually, not erased.

R doubles while C stays fixed. The cutoff frequency…

  1. doubles
  2. halves
  3. stays unchanged
Read more

Cutoff is inversely proportional to the product RC.

Texas Instruments