How do you size a smoothing capacitor?
Use C = I ÷ (f × V_ripple): the load current divided by how often the capacitor is topped up and how much voltage sag you are prepared to accept. A 500 mA load with 1 V of allowable ripple at 100 Hz needs 0.5 ÷ (100 × 1) = 5,000 µF. The ripple frequency is twice the mains frequency for a full-wave rectifier — 100 Hz on a 50 Hz supply, 120 Hz on 60 Hz — because both halves of the waveform recharge the capacitor.
What voltage rating should I choose?
At least 1.5 times the working voltage, and more where the supply is unregulated or spiky. A capacitor run near its rated voltage ages quickly and one run over it can fail spectacularly, since electrolytics can vent or burst. Remember that the peak of a rectified AC waveform is about 1.41 times the RMS value, so a 12 V AC transformer produces around 17 V DC at the capacitor before any load is applied.
Why round up to a standard value?
Because those are the values actually manufactured. The E6 series — 1, 1.5, 2.2, 3.3, 4.7, 6.8 and their decade multiples — covers most electrolytics, and picking the next size up is standard practice rather than over-engineering. Electrolytic tolerances are wide, often −20% to +80%, and capacitance falls as the part ages and dries out, so a component bought at exactly the calculated value may be under it within a few years.
How do I size a capacitor for an RC timing circuit?
Rearrange the time constant: C = τ ÷ R. For a one-second time constant with a 10 kΩ resistor you need 100 µF. Remember that the circuit reaches only 63% of the supply in one time constant, so if your threshold is higher you need to work from the exponential curve rather than τ alone. For timing, prefer film or ceramic capacitors over electrolytics — their tolerance and stability are far better, which matters when the value sets a delay.
Does a bigger capacitor always give better smoothing?
Better ripple, yes, but with real costs. A larger reservoir draws its recharge current in shorter, sharper pulses, which stresses the rectifier diodes and the transformer and produces more heating and electrical noise. It also creates a bigger inrush surge at switch-on, which can trip breakers or weld relay contacts. Beyond a certain point a voltage regulator handles the remaining ripple far more efficiently than simply adding capacitance.