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Time Constant Calculations
52 questions By Tony R. Kuphaldt
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Question 13 of 52
Suppose a capacitor is charged to a voltage of exactly 100 volts, then connected to a resistor so it discharges slowly. Calculate the amount of voltage remaining across the capacitor terminals at the following points in time:
- 1 time constant (τ) after connecting the resistor:
- 2 time constants (2τ) after connecting the resistor:
- 3 time constants (3τ) after connecting the resistor:
- 4 time constants (4τ) after connecting the resistor:
- 5 time constants (5τ) after connecting the resistor:
Reveal answer- 1 time constant (τ) after connecting the resistor: VC = 36.79 volts
- 2 time constants (2τ) after connecting the resistor: VC = 13.53 volts
- 3 time constants (3τ) after connecting the resistor: VC = 4.979 volts
- 4 time constants (4τ) after connecting the resistor: VC = 1.832 volts
- 5 time constants (5τ) after connecting the resistor: VC = 0.6738 volts
Follow-up question: write an equation solving for these voltages at the specified times.
Notes:Although students should be able to look up approximate answers to this question from almost any beginning electronics textbook, the point here is to get them to relate the question to an actual formula so they may calculate this on their own.
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Question 14 of 52
Calculate the voltage across a 470 μF capacitor after discharging through a 10 kΩ resistor for 9 seconds, if the capacitor’s original voltage (at t = 0) was 24 volts.
Also, express this amount of time (9 seconds) in terms of how many time constants have elapsed.
Reveal answerEC = 3.537 volts @ t = 9 seconds.
9 s = 1.915 time constants (1.915τ)
Notes:Here, students must choose which equation to use for the calculation, calculate the time constant for the circuit, and put all the variables in the right place to obtain the correct answer. Discuss all these steps with your students, allowing them to explain how they approached the question.
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Question 15 of 52
Calculate the current through a 250 mH inductor after “charging” through a series-connected resistor with 100 Ω of resistance for 6 milliseconds, powered by a 12 volt battery. Assume that the inductor is perfect, with no internal resistance.
Also, express this amount of time (6 milliseconds) in terms of how many time constants have elapsed.
Reveal answerIL = 109.11 mA @ t = 6 milliseconds
6 ms = 2.4 time constants (2.4τ)
Notes:Here, students must choose which equation to use for the calculation, calculate the time constant for the circuit, and put all the variables in the right place to obtain the correct answer. Discuss all these steps with your students, allowing them to explain how they approached the question.
Maybe this will help someone else. The general formulas for V(t) and I(t) in question 25 (and the x(t) versions in question s 23 and 14) contain typos (or maybe hypertext coding glitches). They should actually be V(t) = (Vf-Vo)(1-e^(-t/𝛕)) + Vo, I(t) = (If-Io)(1-e^(-t/𝛕)) + Io in question 25. Those are correct in the PDF download version. In questions 23 and 24 the equations are x = xinitial + ( xfinal − xinitial ) ( 1 − e[(−t)/(τ)] ).