How to Use the RC Circuit Calculator
An RC circuit combines a resistor (R) and a capacitor (C) in series. When a DC voltage source is connected, the capacitor does not charge instantly — it charges (or discharges) exponentially over time, governed by the circuit's time constant, τ = R × C, measured in seconds when R is in ohms and C is in farads. This calculator finds τ, the capacitor's voltage and the circuit's current at any moment during charging or discharging, and how far through the process the circuit has progressed.
How the calculation works
Enter the resistance and capacitance (each with its own unit selector), the supply voltage (or the capacitor's initial voltage if discharging), the elapsed time since the switch closed, and whether the capacitor is charging or discharging. The calculator converts R and C to base SI units (ohms and farads) and multiplies them to get the time constant τ = RC. For a charging capacitor, voltage rises according to Vc(t) = V(1 − e^(−t/τ)) and current falls according to I(t) = (V/R)e^(−t/τ), starting at V/R and decaying toward zero. For a discharging capacitor, voltage falls according to Vc(t) = V₀e^(−t/τ), and the discharge current follows the same exponential decay from V₀/R. The "Percent Complete" result reports how far the exponential curve has progressed: 1 − e^(−t/τ), expressed as a percentage.
Common mistakes
- Mixing units: resistance and capacitance must be converted to ohms and farads before multiplying — 1 kΩ × 1 µF is not 1, it's 10³ × 10⁻⁶ = 10⁻³ s = 1 ms. Use the unit selectors so the conversion happens automatically.
- Assuming linear charging: a capacitor does not charge at a constant rate. It charges fastest at t = 0 and slows as it approaches the supply voltage — after 1τ it is only about 63.2% charged, not 100%.
- Ignoring how much the timescale can vary: a 1 MΩ resistor with a 1 µF capacitor gives a 1-second time constant, while a 1 Ω resistor with the same capacitor gives a 1-microsecond time constant — component values change circuit speed by orders of magnitude.
Real-world applications
- RC circuits set timing in oscillators, debounce circuits, and camera-flash charge circuits.
- RC low-pass and high-pass filters use the same R and C values to set a cutoff frequency, f_c = 1/(2πRC), that separates signal frequencies.
- Snubber circuits and power-supply smoothing capacitors rely on predictable charge/discharge timing to protect switches and reduce ripple.
- Understanding τ helps size components so a circuit settles fast enough (small τ) or holds a voltage long enough (large τ) for the application.
Frequently Asked Questions
What is the RC time constant?
The RC time constant, τ = R × C, is the time it takes a charging capacitor to reach about 63.2% of the supply voltage, or a discharging capacitor to fall to about 36.8% of its initial voltage. It is measured in seconds when R is in ohms and C is in farads (1 Ω × 1 F = 1 s).
How long does it take a capacitor to fully charge?
Mathematically, a capacitor never reaches exactly 100% — the exponential curve only approaches the supply voltage. In practice, a capacitor is considered fully charged (or discharged) after about 5 time constants (5τ), by which point it has reached over 99% of its final voltage.
How do I find the voltage across a capacitor at a specific time?
For a charging capacitor, use Vc(t) = V(1 − e^(−t/RC)), where V is the supply voltage. For a discharging capacitor, use Vc(t) = V0 × e^(−t/RC), where V0 is the capacitor's voltage at the moment it started discharging.
What is the cutoff frequency of an RC filter?
For a simple RC low-pass or high-pass filter, the cutoff (-3 dB) frequency is f_c = 1/(2πRC). The same R and C values that set the time-domain time constant also set the filter's frequency response.
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |