RC Circuit Calculator

An RC circuit is a fundamental electrical circuit consisting of a resistor (R) connected in series with a capacitor (C). It is widely used in filters, timing circuits, and signal processing. The behavior of the circuit is governed by how quickly the capacitor charges or discharges through the resistor.

The time constant τ (tau) equals R × C and represents the time it takes for the capacitor to charge to approximately 63.2% of the supply voltage (or discharge to 36.8% of its initial voltage). After 5 × τ, the capacitor is considered fully charged or discharged (>99%).

Not exactly. The time constant τ is a single characteristic value (R × C), while the full charging time is typically taken as 5τ — the point at which the capacitor reaches over 99% of the supply voltage. The time constant is the most important single figure because it defines the rate of the exponential charge/discharge curve.

The cutoff (or characteristic) frequency is f = 1 / (2π × R × C). At this frequency, the output signal of an RC filter is attenuated to 70.7% (−3 dB) of its input. Below this frequency, a low-pass RC filter passes the signal; above it, the signal is attenuated.

Capacitive reactance (Xc) is the opposition a capacitor presents to alternating current at the cutoff frequency, calculated as Xc = 1 / (2π × f × C). It is measured in ohms and decreases as frequency increases — meaning a capacitor passes high-frequency signals more easily than low-frequency ones.

The energy stored in a capacitor is E = ½ × C × V², where C is the capacitance in farads and V is the voltage across the capacitor in volts. The result is in joules. A larger capacitance or higher voltage means significantly more stored energy, since voltage is squared in the formula.

In a charging circuit, the capacitor voltage rises from 0 toward the supply voltage following V(t) = Vs × (1 − e^(−t/τ)). In a discharging circuit, the capacitor releases stored energy and voltage falls from its initial value toward zero following V(t) = V0 × e^(−t/τ). Both processes follow the same time constant τ = RC.

Yes. An RC circuit can function as a low-pass filter (passing low frequencies and blocking high frequencies) or a high-pass filter, depending on where the output voltage is measured. The cutoff frequency f = 1/(2πRC) marks the boundary between the passband and the stopband.