Q: What is a time constant?

A: The time constant is a numerical value that serves as a guideline for the time it takes for a change to reach a steady state. In an RC circuit, the time constant τ is expressed as τ = RC.

Q: How does the capacitor voltage change during charging and discharging?

A: During charging, V = Vo × (1 − e^(−t/RC)); during discharging, V = Vo × e^(−t/RC). At time τ, the voltage reaches approximately 63.2% during charging and 36.8% during discharging.

Q: How to calculate the time to reach a specified voltage?

A: For charging: Tn = CR × ln(V / (V − Vn)); for discharging: Tn = CR × ln(V / Vn).

Calculating the time constant | Nippon Chemi-Con Corporation

Calculating the time constant

Time Constant Calculation

The time constant is a numerical value that indicates how long it takes for a change to reach a steady state.
It is denoted by τ (tau), and in an RC circuit, τ is given by the following equation:

Definition of Time Constant

\(\tau = RC\)

R: : Resistance (Ω)
C: : Capacitance (F)

Voltage Change During Charging and Discharging

In an RC circuit, the capacitor voltage V after t seconds of charging, with power supply voltage Vo, is given by:

\(V = V_{o} \left(1 - e^{\frac{-t}{\tau}}\right)\)

Substituting τ = RC:

\(V = V_{o} \left(1 - e^{\frac{-t}{RC}}\right)\)

When time t = RC:

\(V = V_{o} \left(1 - e^{-1}\right)\)

Since e is the base of the natural logarithm:

\(V = V_{o} \left(1 - \frac{1}{2.7182...}\right)\)

\(V \approx 0.632 V_{o}\)

That is, when time t = τ, the capacitor voltage V reaches approximately 63.2% of the power supply voltage.
Furthermore, when t = 5τ:

\(V \approx 0.993 V_{o}\)

It becomes nearly equal to the power supply voltage.
On the other hand, during discharging, the capacitor voltage V after t seconds is given by:

\(V = V_{o} \cdot e^{\frac{-t}{\tau}}\)

When t = τ:

\(V = V_{o} \cdot e^{-1}\)

\(V \approx V_{o} \cdot 0.368\)

That is, after time τ, the voltage drops to approximately 36.8% of the initial voltage Vo.

Time to Reach Specified Voltage

Charging: Time to reach a specified voltage

\(T_n = CR \cdot \ln\left(\frac{V}{V - V_n}\right)\)

Discharging: Time to reach a specified voltage

\(T_n = CR \cdot \ln\left(\frac{V}{V_n}\right)\)

If you have any questions or inquiries that do not apply to the above, please contact us at the following address.

Products Inquiries

NIPPON CHEMI-CON CORPORATION

FAQ/Contact usProducts FAQs

Calculating the time constant

Time Constant Calculation

Definition of Time Constant

Voltage Change During Charging and Discharging

Time to Reach Specified Voltage