The time constant
- The time constant of a capacitor discharging through a resistor is a measure of how long it takes for the capacitor to discharge
- The time constant is defined as:
The time taken for the charge, current or voltage of a discharging capacitor to decrease to 37% of its original value
- This is represented by the Greek letter tau () and measured in units of seconds (s)
- It is a useful way of comparing the rate of change of similar quantities e.g. charge, current or p.d.
- The time constant is defined by the equation:
= RC
- Where:
- = time constant (s)
- R = resistance of the resistor (Ω)
- C = capacitance of the capacitor (F)
- For example, to find the time constant from a voltage-time graph, calculate 0.37V0 and determine the corresponding time for that value
Time constant on a capacitor discharge graph
The time constant shown on a discharging capacitor for potential difference
Worked example
A capacitor of 7 nF is discharged through a resistor of resistance R. The time constant of the discharge is 5.6 × 10-3 s.
Calculate the value of R.
Answer:
Step 1: Write out the known quantities
- Capacitance, C = 7 nF = 7 × 10-9 F
- Time constant, = 5.6 × 10-3 s
Step 2: Write down the time constant equation
= RC
Step 3: Rearrange for resistance R
Step 4: Substitute in values and calculate R