How long does a capacitor take to fully charge?

A capacitor is considered fully charged after 5 time constants (5τ), at which point it has reached 99.3% of the supply voltage. In practice engineers treat 5τ as effectively fully charged for most applications.

What is the cutoff frequency of an RC filter?

The -3dB cutoff frequency of an RC low-pass or high-pass filter is fc = 1 / (2π × R × C). At this frequency the output voltage is 70.7% of the input (−3 dB). Signals below fc pass through a low-pass filter; signals above fc pass through a high-pass filter.

What is the difference between RC and RL time constants?

An RC circuit uses a resistor and capacitor: τ = R × C. An RL circuit uses a resistor and inductor: τ = L / R. Both describe the time to reach 63.2% of the final value. RC circuits store energy in an electric field; RL circuits store energy in a magnetic field. The cutoff frequency for RL is fc = R / (2πL).

RC Time Constant Calculator – Charge & Discharge Curve

Q: What is the RC time constant?

The RC time constant (τ, tau) is the product of resistance (R) in ohms and capacitance (C) in farads. τ = R × C gives the time in seconds for the capacitor to charge to approximately 63.2% of the supply voltage, or discharge to 36.8% of its initial voltage.

RC Circuit Inputs

Resistance (R)

Capacitance (C)

Supply Voltage Vs (V)

Initial Voltage V₀ (V)

Mode

τ = — ms

Cutoff Freq

—

Energy Stored

—

Charge Q

—

Time to Voltage Percentage

Target %	Time Constant	Time

Note: A capacitor is considered fully charged at 5τ (99.3%). Times shown assume ideal exponential charge/discharge with a linear resistor.

What is the RC Time Constant?

The RC time constant (τ, pronounced "tau") is a fundamental parameter in electronics that describes how quickly a capacitor charges or discharges through a resistor. It is defined as:

τ = R × C

Where R is in ohms (Ω) and C is in farads (F), giving τ in seconds. After one time constant, the capacitor charges to 63.2% of the supply voltage (or discharges to 36.8% of its initial voltage). This universal behaviour is a direct result of the exponential nature of capacitor charging.

Charging: V(t) = Vs × (1 − e^−t/τ)
Discharging: V(t) = V₀ × e^−t/τ

RC circuits are used as filters, timing circuits (555 timer), integrators, differentiators, and sample-and-hold circuits in virtually every branch of electronics.

Charge and Discharge Percentage Table

Time	Charging Voltage %	Discharging Voltage %
1τ 63.2%	63.2%	36.8%
2τ	86.5%	13.5%
3τ	95.0%	5.0%
4τ	98.2%	1.8%
5τ Full	99.3%	0.7%

The 63.2% figure at 1τ comes from 1 − e⁻¹ = 1 − 0.368 = 0.632. Engineers commonly use 5τ as the fully charged threshold because 99.3% is within measurement noise for most practical purposes.

RC Filter Cutoff Frequency

An RC network forms a first-order low-pass or high-pass filter with a -3dB cutoff frequency of:

f_c = 1 / (2π × R × C) = 1 / (2π × τ)

At this frequency the output amplitude is 70.7% of the input (−3 dB). Frequencies below f_c pass through a low-pass RC filter; frequencies above f_c are attenuated. Common uses include anti-aliasing filters before ADCs, audio tone controls, and power supply noise filtering.

Frequently Asked Questions

The RC time constant (τ) is the product of resistance R (ohms) and capacitance C (farads), giving a time in seconds. It represents the time for the capacitor to charge to 63.2% of the supply voltage, or discharge to 36.8% of its initial voltage. The formula is simply τ = R × C.

A capacitor is considered fully charged after 5 time constants (5τ), reaching 99.3% of the supply voltage. Theoretically it never reaches exactly 100% due to the asymptotic nature of the exponential function, but 5τ is the accepted engineering threshold for "fully charged" in virtually all applications.

The -3dB cutoff frequency is f_c = 1 / (2πRC). At this frequency the output voltage drops to 70.7% of the input (a power reduction of exactly half, or -3 dB). Below f_c a low-pass filter passes signals; above f_c a high-pass filter passes signals.

An RC circuit uses a resistor and capacitor: τ = R × C. An RL circuit uses a resistor and inductor: τ = L / R. Both time constants describe the time to reach 63.2% of the final steady-state value. RC circuits store energy in an electric field (voltage across capacitor); RL circuits store energy in a magnetic field (current through inductor). The RL cutoff frequency is f_c = R / (2πL).