Resistance (R): ฮฉ Capacitance (C): F Time Constant (ฯ): sRC Time Constant Calculator
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What is an RC Circuit?
An RC circuit containing a resistor (R) and capacitor (C) is connected in series to power sources, and are fundamental in modern electronics. Resistors slow down current, while capacitors store electrical energy. These components work together to create accurate timing and filtering effects, controlling how fast the capacitor charges/discharges.
The RC Time Constant
The RC time constant (ฯ) measures how quickly a capacitor charges or discharges in an RC circuit. It determines how quickly the circuit responds to changes.
Formula:
ฯ = R ร C
- ฯ: Time constant (seconds)
- R: Resistance (ohms, ฮฉ)
- C: Capacitance (farads, F)
How Does It Work?
- Charging: When power is applied, the capacitor charges up to about 63% of its maximum voltage after a one-time constant (ฯ).
- Discharging: When power is removed, the capacitor loses approximately 63% of its charge after a one-time constant (ฯ).
After 5 time constants (5ฯ), the capacitor is considered fully charged or discharged.
Charging and Discharging Equations
The voltage across the capacitor during charging and discharging can be calculated using these formulas:
Charging:
V(t) = Vfinal ร (1 – e-t/ฯ)
Discharging:
V(t) = Vinitial ร e-t/ฯ
Where:
- V(t): Voltage at time t
- Vfinal: Final voltage during charging
- Vinitial: Initial voltage during discharging
- t: Time in seconds
- ฯ: Time constant (R ร C)
Example 1: Charging a Capacitor
- Resistance (R) = 10 kฮฉ = 10,000 ฮฉ
- Capacitance (C) = 100 ยตF = 0.0001 F
- Time Constant (ฯ) = R ร C = 10,000 ร 0.0001 = 1 second
Example 2: Discharging a Capacitor
- Resistance (R) = 1 Mฮฉ = 1,000,000 ฮฉ
- Capacitance (C) = 10 nF = 0.00000001 F
- Time Constant (ฯ) = 1,000,000 ร 0.00000001 = 0.01 seconds (10 ms)
Charging Behavior
| Time (t/ฯ) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Voltage (%) | 63.2% | 86.5% | 95.0% | 98.2% | 99.3% |
Discharging Behavior
| Time (t/ฯ) | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Voltage (%) | 36.8% | 13.5% | 5.0% | 1.8% | 0.7% |
Applications of RC Circuits
- Timing circuits (delays, oscillators)
- Filtering signals (low-pass, high-pass filters)
- Power supply smoothing
- Analog-to-digital converters (ADCs)
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