Charging and discharging a capacitor
Why does charging slow down? Predict, throw the switch and measure the trace. Then choose a resistance to prepare a flash in under two seconds.
Throw the switch by hand, turn the resistance box's knob, drag the cursor across the screen to measure, and turn the oscilloscope's left-hand knob to change the timebase. Click a name or an object to look closer, double-click the bench to step back. Slide the view with shift + scroll, the arrow keys, a right-button drag or two fingers.
Three checks before closing the circuit: polarity, working voltage, and a capacitor that starts empty.
Journey and readings
Model used
- Ideal supply: 6.00 V whatever the current, no internal resistance.
- Perfect wires and switch: no resistance, instantaneous switching.
- Voltmeter and oscilloscope with no effect on the circuit: infinite input impedance, they draw no current.
- No leakage or series resistance: an isolated capacitor holds its voltage. Connected across R, it discharges.
- Exact resistance box: 1 kΩ, 2.2 kΩ, 4.7 kΩ and 10 kΩ with no tolerance.
- No measurement noise: the curves are the equations, computed exactly.
- The capacitor printed 470 µF is really 442 µF: an electrolytic component is sold at ±20 %, just like in a real lab.
- The moving-coil voltmeter has its inertia and the digital readout takes a moment to settle, like real instruments.
Oscilloscope
Place the cursor where the trace meets the dashed marker. Arrow keys adjust time in 0.01 s steps.
Measurement, equations and energy
- C nominal
- 470 µF ± 20 %
- τ = R × C nominal
- 1.03 s
- τ from cursor
- —
- Gap from nominal
- —
- W = ½ C uC²
- 0.00 mJ
Charge: i = (E − uC) / R. Discharge: i = −uC / R. The negative sign indicates reversed current. In both cases: i = C × duC/dt.
uC(t) = Uf + (Ui − Uf) exp(−t/RC), with Uf = E during charge and 0 during discharge. At τ, 63.2% of the change is complete; at 5τ, 99.3%. Final voltage does not depend on R.
Noiseless simulated trace, sampled approximately every 0.02 s. Cursor display resolution is 0.01 s, not a guarantee of accuracy. The gap from the nominal calculation also reflects the component’s actual capacitance. Displayed energy uses that actual capacitance.
Changing the timebase scales the view without changing the circuit. A new acquisition records at least 5τ; switching during charging preserves capacitor voltage.