RC Formulas
Time constant τ = R × C (in seconds, with R in ohms and C in farads). Charging: V(t) = Vs × (1 - e^(-t/τ)). Discharging: V(t) = V0 × e^(-t/τ). Cutoff frequency f = 1 / (2π × τ) Hz. The capacitor reaches 99.3% of its final value at 5τ.
Frequently Asked Questions
The RC time constant (τ, tau) is the time it takes for a capacitor to charge to 63.2% of the supply voltage through a resistor, or discharge to 36.8% of its initial voltage. τ = R × C. The capacitor is considered fully charged or discharged after 5τ (99.3% of final value).
Charging: V(t) = Vs × (1 - e^(-t/τ)). Discharging: V(t) = V0 × e^(-t/τ). Where Vs is supply voltage, V0 is initial voltage, t is time in seconds, and τ = R × C.
The -3dB cutoff frequency of an RC filter is f = 1/(2π×R×C). At this frequency, the output is attenuated to 70.7% of the input (−3dB). For a low-pass RC filter, frequencies above fc are attenuated; for a high-pass RC filter, frequencies below fc are attenuated.
In a low-pass RC filter, the output is taken across the capacitor. Low frequencies pass easily; high frequencies are attenuated. In a high-pass filter, the output is taken across the resistor. High frequencies pass easily; low frequencies are attenuated. The cutoff frequency is the same formula for both.
Only resistance (Ω) and capacitance (Farads) determine τ. Temperature can affect both components: capacitor values drift with temperature (especially ceramic capacitors), and resistor values have a temperature coefficient (PPM/°C). High-precision RC timing circuits use temperature-stable components (NP0/C0G capacitors, metal film resistors).
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