IB DP Physics: HL复习笔记11.3.4 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

  • 19.2-Time-Constant-Graph

The graph of voltage-time for a discharging capacitor showing the positions of the first three time constants

  • 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

Exam Tip

Note that the time constant is not the same as half-life. Half-life is how long it takes for the current, charge or voltage to halve whilst the time constant is to 37% of its original value (not 50%).

Although the time constant is given on the datasheet, you will be expected to remember the half-life equation t1/2 = 0.69RC

Problems Involving the Time Constant

  • Problems involving the time constant tend to involve
    • Calculations
    • Determining the time constant from a graph
  • To find the time constant from a voltage-time graph, calculate 0.37V0 and determine the corresponding time for that value

7.7.2-Time-Constant-on-Graph

The time constant shown on a charging and discharging capacitor

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.

7.7.2-Time-Constant-Worked-Example-1

 

 

 

 

 

 

转载自savemyexams

更多IB课程
翰林国际教育资讯二维码