Time Constant Calculator

Calculator

Resistance (Ω)

Capacitance

Time Constant (τ)

0.000 ms

τ = R × C

Time to Steady State (5τ)

0.000 ms

Complete charge/discharge at ~99.3%

Charge Distribution:

1τ 63.2%

2τ 86.5%

3τ 95.0%

4τ 98.2%

5τ 99.3%

Charging Curve (RC)

Formula: τ = R × C
Represents the time for a capacitor to charge to ~63.2% of supply voltage.

Practice Problems

Problem 1

Given R = 10 kΩ and C = 100 μF, find the time constant (τ) and the time required for full charge (5τ).

Solution:

τ = R × C = 10,000 Ω × 100×10⁻⁶ F = 1 second
Time to steady state = 5τ = 5 seconds
After 1 second: 63.2% charged
After 5 seconds: 99.3% charged (practical completion)

Problem 2

An RL circuit has R = 50 Ω and L = 500 mH. Calculate τ and identify what percentage of current flows at t = τ and t = 3τ.

Solution:

τ = L / R = 0.5 H / 50 Ω = 0.01 seconds (10 ms)
At t = τ: Current = 63.2% of final value
At t = 3τ: Current = 95.0% of final value
The inductor initially opposes current flow, then gradually allows full current.

Problem 3

A capacitor must charge to 86.5% in 2 seconds. If R = 5 kΩ, what must C be (in microfarads)?

Solution:

86.5% charge occurs at t = 2τ
So: 2τ = 2 seconds, therefore τ = 1 second
τ = R × C
1 = 5,000 × C
C = 1/5,000 = 0.0002 F = 200 μF

Time Constant Calculator

Calculator

Charging Curve (RC)

Circuit Diagram

Practice Problems

Important Disclaimer