DP IB Physics: HL

Revision Notes

Syllabus Edition

First teaching 2014

Last exams 2024

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11.3.4 The Time Constant

Test Yourself

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 over e (where e is the exponential function) multiplied by the original value (I0, Q0 or V0)
    • This is represented by the Greek letter tau, 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:

tau = RC

  • Where:
    • tau = time constant (s)
    • R = resistance of the resistor (Ω)
    • C = capacitance of the capacitor (F)

Time Constant Graph, downloadable AS & A Level Physics revision notes

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

  • This can also be written in terms of the time constant, tau:

t1/2 = ln(2) tau ≈ 0.69 tau = 0.69 RC

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

Time Constant on Graph, downloadable AS & A Level Physics revision notes

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.

Time Constant Worked Example

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Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.