RC Time Constant

The time constant τ tells you how quickly an RC circuit responds to a change in voltage. It is the product of resistance and capacitance because the resistor controls how fast charge can flow, while the capacitor sets how much charge is needed to change the voltage; together they determine the circuit's characteristic timescale. After one time constant, a charging capacitor has reached about 63.2% of its final voltage, and a discharging one has dropped to about 36.8% of its starting value.

Use this formula when analyzing how long a capacitor takes to charge or discharge through a resistor, such as in timing circuits, filters, sensor interfaces, and delayed switching circuits. It is also useful whenever you need the response speed of a first-order electrical circuit.

• Forgetting to convert kilo-ohms and microfarads into ohms and farads before multiplying
• Using the time constant as the total charge or total discharge time instead of a characteristic timescale
• Confusing τ = RC with formulas for voltage across the capacitor during charging or discharging