AQA A Level Physics復習筆記7.7.2 The Time Constant
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 definition of the time constant is:
The time taken for the charge, current or voltage of a discharging capacitor to decrease to 37% of its original value
- Alternatively, for a?charging?capacitor:
The time taken for the charge or voltage of a charging capacitor to rise to 63% of its maximum value
- 37% is 0.37 or 1 / e (where e is the exponential function) multiplied by the original value (I0,?Q0?or?V0)
- This is represented by the Greek letter tau,
and measured in units of seconds?(s) - The time constant provides an easy way to compare the rate of change of similar quantities eg. charge, current and p.d.
- It is defined by the equation:
- For example, to find the time constant from a voltage-time graph, calculate 0.37V0?and determine the corresponding time for that value
The time constant shown on a charging and discharging capacitor
- The time to half, t1/2?(half-life) for a discharging capacitor is:
The time taken for the charge, current or voltage of a discharging capacitor to reach half of its initial value
- This can also be written in terms of the time constant:
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.
Exam Tip
Remember to check the context of an exam question, i.e., whether the capacitor is?charging?or?discharging. The definition of the time constant depends on it!
- For a?charging?capacitor, the time constant refers to the time taken to reach 63% of its?maximum?potential difference or charge stored
- For a?discharging?capacitor, the time constant refers to the time take to discharge to 37% of its?initial?potential difference or charge stored
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