Resistor + capacitor
Catch time in a circuit.
A capacitor’s voltage cannot jump instantly. Watch it charge, disconnect the source and follow the stored energy.
- RC · Resistor–capacitor circuit
- Resistor–capacitor. R means resistance, C means capacitance. Together they set how quickly the capacitor voltage changes.
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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The resistor sets the pace.
Ideal RC circuit, 5 V source. Disconnecting switches the resistor to common to provide a discharge path. Leakage and ESR are omitted.
Delay module = resistor + capacitor. Time constant τ = R × C. After τ, voltage travels about 63% toward its new value; after 5τ, over 99%. Discharge energy becomes heat in the resistor. Without a discharge path, behaviour is different.
Difficulty
Build · Store some charge
Power on and wait until capacitor voltage exceeds 3 V.
Need a hint?
10 kΩ and 100 µF give a time constant of 1 second.
Explore · Slow time down
Choose R and C for a time constant of 2–3 seconds. Start charging.
Need a hint?
Convert kΩ to Ω and µF to F: 20,000 × 0.0001 = 2 seconds.
Solve it · Store and release
Set τ to 3–5 seconds. Charge above 4 V, disconnect, then check during discharge between 1 and 3 V.
Need a hint?
A longer time constant gives you more time to check the discharge.
Extra reading and circuit recipes
Give a circuit a sense of time
A capacitor stores energy in an electric field between conductors. Its voltage cannot jump instantly without an impulse of current. Pair it with a resistor and a sudden change becomes a gradual curve: a tiny circuit can now remember what happened a moment ago.
τ = R × C → 10,000 Ω × 100 µF = 1 s
For a step from 0 to Vs, Vc(t) = Vs × (1 − e^(−t/τ)). During discharge to ground, Vc(t) = Vstart × e^(−t/τ). In this lab, Power off connects the resistor to 0 V so the capacitor can discharge.
63%, not 100%
After one time constant, a capacitor charging from zero reaches about 63.2% of its final voltage. After five time constants it reaches about 99.3%.
The last bit is the slowest
As capacitor voltage approaches the supply, less voltage remains across the resistor. Current shrinks, so charging slows down.
Energy grows with voltage squared
Stored energy is E = ½CV². At the same capacitance, doubling voltage stores four times as much energy.
A useful trap to avoid
Opening a switch and disconnecting everything is different from connecting to ground. An isolated ideal capacitor keeps its charge. Real capacitors leak, and an added load changes the discharge curve.
You double R while keeping C unchanged. Charging becomes…
- twice as slow
- twice as fast
- unchanged
Read more
The time constant R × C doubles. Reaching the same fraction of the final voltage takes twice as long.
A slow memory
Watch a voltage build for several seconds.
τ = 4.4 s. About 22 s reaches 99.3% of 5 V.
A quick response
Compare this curve with the slow memory.
τ = 0.10 s. The capacitor is nearly charged after half a second.