Calculating Capacitor Discharge Time

Capacitor Discharge Time Formula:

\[ t = -R \times C \times \ln\left(\frac{V_t}{V_0}\right) \]

Resistance (R):

Capacitance (C):

Voltage at Time t (V_t):

Initial Voltage (V_0):

Discharge Time (t):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Capacitor Discharge Time?

The capacitor discharge time represents how long it takes for a capacitor to discharge from its initial voltage to a specified lower voltage through a resistor. This is an important parameter in electronic circuit design and timing applications.

2. How Does the Calculator Work?

The calculator uses the capacitor discharge equation:

\[ t = -R \times C \times \ln\left(\frac{V_t}{V_0}\right) \]

Where:

\( t \) — Discharge time (seconds)
\( R \) — Resistance (ohms)
\( C \) — Capacitance (farads)
\( V_t \) — Voltage at time t (volts)
\( V_0 \) — Initial voltage (volts)

Explanation: The equation calculates the time required for a capacitor to discharge from its initial voltage V₀ to a specified voltage Vₜ through a resistor R.

3. Importance of Discharge Time Calculation

Details: Accurate discharge time calculation is crucial for designing timing circuits, power supply systems, and any application where controlled energy release from capacitors is required.

4. Using the Calculator

Tips: Enter resistance in ohms, capacitance in farads, and both voltages in volts. All values must be positive, and Vₜ must be less than V₀ for discharge to occur.

5. Frequently Asked Questions (FAQ)

Q1: What is the time constant (τ) in RC circuits?
A: The time constant τ = R × C represents the time it takes for the capacitor to discharge to approximately 36.8% of its initial voltage.

Q2: How does resistance affect discharge time?
A: Higher resistance values result in longer discharge times as they limit the current flow from the capacitor.

Q3: How does capacitance affect discharge time?
A: Larger capacitance values store more charge and therefore take longer to discharge through the same resistance.

Q4: What happens if V_t is greater than V_0?
A: The equation would give a negative time result, which is physically impossible. V_t must always be less than V_0 for discharge calculations.

Q5: Is this formula applicable to all capacitor types?
A: This formula applies to ideal capacitors. Real capacitors may have additional factors like equivalent series resistance (ESR) that affect discharge characteristics.