Capacitor Charge & Time Constant Calculator
To create a table about capacitor charge and time constant, we need to understand the relationship between these concepts. The key parameters involved in a charging capacitor are:
- Capacitance (C): Measured in farads (F), it's the ability of a capacitor to store charge.
- Resistance (R): Measured in ohms (Ω), it controls the rate at which the capacitor charges.
- Time constant (τ): The product of resistance and capacitance, τ = R × C, measured in seconds (s).
- Voltage across the capacitor (V): The voltage at any time during the charging process.
- Initial voltage (V₀): The voltage across the capacitor when it starts charging.
- Charging equation: V(t) = V₀(1 - e^(-t/τ)), where t is time in seconds.
The time constant (τ) is a key measure that determines how fast the capacitor charges. At t = τ, the capacitor will charge up to about 63.2% of its full voltage.
Here’s a table showing the relationship between time (t), voltage across the capacitor (V), and the time constant (τ):
| Time (t) | Voltage (V) | Time Constant (t/τ) | Percent Charged (%) |
|---|---|---|---|
| 0 | 0 | 0 | 0% |
| τ | 0.632 V₀ | 1 | 63.2% |
| 2τ | 0.865 V₀ | 2 | 86.5% |
| 3τ | 0.950 V₀ | 3 | 95.0% |
| 4τ | 0.982 V₀ | 4 | 98.2% |
| 5τ | 0.993 V₀ | 5 | 99.3% |
Key Points:
- Time Constant (τ): After one time constant, the capacitor is charged to 63.2% of its final value.
- 5τ Rule: After 5 time constants, the capacitor is considered almost fully charged (99.3%).