RC Circuits
Charge/discharge curve. Builds on Capacitance and Ohm's Law.
You connect a 10 kΩ resistor and a 100 µF capacitor in series with a 9 V battery. The capacitor starts completely uncharged. You close the switch and start a stopwatch.
After exactly one time constant (τ = RC = 1 second), what fraction of the final voltage appears across the capacitor?
After one time constant, the capacitor reaches about 63% of its final voltage! The charging is exponential, not linear. V(t) = V₀(1 − e^(−t/RC)). At t = τ, e⁻¹ ≈ 0.37, so V ≈ 0.63 × V₀. The current starts high and decays — like water flowing into a tank that gets harder to fill as the pressure builds up.
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Close the switch and watch the capacitor charge. The voltage curve rises steeply at first, then bends over as it approaches the battery voltage. The current curve does the opposite — it starts high and decays to zero. Look for the τ marker at 63%!
V(t) = V₀(1 − e^(−t/RC))
The time constant τ = RC sets the pace. Big R or big C means slow charging. After 1τ: 63%. After 5τ: 99%. The same τ governs discharge too.
A camera flash charges a large capacitor over several seconds (that’s the whine you hear), then dumps all the energy in a millisecond burst of light. The RC time constant determines how long you wait between flashes.
A defibrillator charges a capacitor to thousands of volts, then delivers the energy to the heart in milliseconds. The RC time constant of the body + capacitor determines the pulse shape.
Capacitive touch screens detect your finger by measuring tiny changes in RC time constants. Your finger adds capacitance to the circuit, changing the charging time.
RC circuits are the building blocks of audio equalizers. Low-pass filters use RC to smooth out high frequencies; high-pass filters block the bass. Every audio system uses RC circuits.
“The RC circuit is where electricity meets time. The time constant τ = RC tells you how fast energy can flow in or out — and that single number shapes everything from camera flashes to the beating of a defibrillated heart.”
RC Circuit Lab
Build your own RC circuit and explore how resistance and capacitance control the charging and discharging curves. Watch voltage and current evolve in real time, and see how the time constant shapes everything.
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Start with a small R and C to see fast charging. Now increase R by 10× — the time constant stretches out and the capacitor charges much more slowly. Try switching to discharge mode and watch the exponential decay. Toggle the square wave input to see repeated charge/discharge cycles. Find the 63% and 37% markers on the graph — they always land right at t = τ.
The RC time constant is one of the most fundamental timescales in electronics. It sets the speed limit for how fast a circuit can respond. Every digital chip, every sensor, every filter in your phone is governed by RC time constants.