The RC time constant (τ) is the time required to charge a capacitor through a resistor to approximately 63.2% of the supply voltage. It is given by the product of resistance (R) and capacitance (C). This calculator computes the time constant, cutoff frequency, and voltage at specific time intervals. Essential for filter design, timing circuits, and pulse shaping.
📐 RC Circuit Formulas
Time Constant: τ = R × C (seconds) Cutoff Frequency: f_c = 1 / (2π × τ) (Hz) Charging Voltage: Vc(t) = Vf × (1 - e^(-t/τ)) Discharging Voltage: Vc(t) = Vi × e^(-t/τ)
Where: R = Resistance (Ω) C = Capacitance (F) τ = Time Constant (s) f_c = Cutoff Frequency (Hz) Vf = Final Voltage Vi = Initial Voltage
📊 RC Time Constant Reference
RC Combination
τ (seconds)
f_c (Hz)
Application
100Ω / 100µF
0.010
15.9
Power supply filtering
1kΩ / 100µF
0.100
1.59
Audio filtering
10kΩ / 10µF
0.100
1.59
Timing circuits
100kΩ / 1µF
0.100
1.59
Low frequency filters
1MΩ / 0.1µF
0.100
1.59
Long timing
10kΩ / 100nF
0.001
159
High pass filter
📌 Charge/Discharge Percentages
1τ (63.2%): Charged to 63.2% of final voltage
2τ (86.5%): Charged to 86.5% of final voltage
3τ (95.0%): Charged to 95.0% of final voltage
4τ (98.2%): Charged to 98.2% of final voltage
5τ (99.3%): Considered fully charged
💡 Applications of RC Circuits
Low-Pass Filters: Pass low frequencies, block high frequencies
High-Pass Filters: Pass high frequencies, block low frequencies
Integrators: Used in analog computers and signal processing
Differentiators: Used for edge detection and waveform shaping
Power Supply Filtering: Smoothing rectified AC voltage
❓ Frequently Asked Questions (FAQ)
❓ What is the RC time constant? ▼
The RC time constant (τ) is the time required to charge a capacitor to 63.2% of the supply voltage through a resistor. It is calculated as τ = R × C, where R is in ohms and C is in farads.
❓ How long does it take to fully charge a capacitor? ▼
A capacitor is considered fully charged after 5 time constants (5τ), reaching about 99.3% of the supply voltage. For practical purposes, 5τ is used.
❓ What is the cutoff frequency of an RC circuit? ▼
The cutoff frequency (f_c) is the frequency at which the output voltage drops to 70.7% of the input voltage. It is calculated as f_c = 1 / (2π × R × C).
❓ What is the difference between low-pass and high-pass RC filters? ▼
Low-pass filters pass low frequencies and attenuate high frequencies (output across capacitor). High-pass filters pass high frequencies and attenuate low frequencies (output across resistor).
❓ What happens at t = τ in an RC circuit? ▼
At t = τ, the capacitor voltage reaches 63.2% of the final voltage. The charging current drops to 36.8% of its initial value.
❓ What is the unit of time constant? ▼
The time constant is measured in seconds (s). With R in ohms (Ω) and C in farads (F), τ = Ω × F = seconds.