What is Time constant: Definition and 147 Discussions

In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system.
In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at low frequencies.
The time constant is also used to characterize the frequency response of various signal processing systems – magnetic tapes, radio transmitters and receivers, record cutting and replay equipment, and digital filters – which can be modeled or approximated by first-order LTI systems. Other examples include time constant used in control systems for integral and derivative action controllers, which are often pneumatic, rather than electrical.
Time constants are a feature of the lumped system analysis (lumped capacity analysis method) for thermal systems, used when objects cool or warm uniformly under the influence of convective cooling or warming.Physically, the time constant represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate, because of the progressive change in the rate of decay the response will have actually decreased in value to 1 / e ≈ 36.8% in this time (say from a step decrease). In an increasing system, the time constant is the time for the system's step response to reach 1 − 1 / e ≈ 63.2% of its final (asymptotic) value (say from a step increase). In radioactive decay the time constant is related to the decay constant (λ), and it represents both the mean lifetime of a decaying system (such as an atom) before it decays, or the time it takes for all but 36.8% of the atoms to decay. For this reason, the time constant is longer than the half-life, which is the time for only 50% of the atoms to decay.

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  1. skibidi

    Find current in a RL circuit

    I found the time constant using L/R and got 0.62s (3.6H/5.8ohms) I found the initial current V/R and got 4.086A (23.7V/5.8ohms) I(f) = 4.086A(1-e^(-0.5s/0.62s)) Then I plugged it into the equation and got 2.26A and it was wrong
  2. abdulbadii

    I Outright understanding L/R inductor time constant

    How is the real understanding, when an external constant E potential (voltage) is imposed/applied on a LR circuit, that is being charged as the characteristic L/R inductor time constant: the greater R the shorter time inductor get (full) charged This absolutely independent to the E; it could...
  3. T

    Measuring time constant using an inductor with a core vs. no core

    I'm doing a simple RL Circuit Lab where students use 800- and 1600-turn air core coils to measure the time constant. Experimental results very nicely agree with predicted results. However, when students insert a steel (or iron) core in the coils, experimental results are far different than...
  4. boysenbeary

    Engineering Finding Time Constant T Without L for an LR Circuit

    Edit: Picture of the Circuit (Simple RL circuit) The value of L is not given. Attempt to Solve for T by Rearranging Equation 1: I rearranged the equation to solve for T, using Ohm's Law so solve for I = V/R at each time. https://www.desmos.com/calculator/qlb2n6w4bg This graph is...
  5. greg_rack

    Time constant of a discharge RC circuit, capacity and charge

    So, the only thing which came to my mind in order to solve this problem was actually to write down the equations using the discharge function, being given two instants and their corresponding charges... but doing so I'm unable to find anything. Ideally, I'd say I should find the time constant...
  6. G

    Questions on Capacitors again

    Well i don't you to solve the question for me but I want you to clarify the concepts pertaining to this question. My question is how do I write a equation for the circuit since the there is same charge on one of the capacitors. While writing the equation should i put the voltage across the...
  7. E

    Proving time constant formulas of a capacitor using Kirchoff's laws

    the attached files are a diagram of the circuit. also I believe I figured out how to proof equation (7) but I'm lost on how to proof (8)
  8. B

    Time constant question in an AQA exam paper

    I assumed that i had to take 5 time constants which would give the time taken to charge fully i assume then divide by 10 giving me a total number of readings of 34 , the answer is 6 yet they only used a single time constant to determine the number of readings? as this give me an answer of 68 or...
  9. Abo

    Time constant of a Toroidal Solenoid

    Is my solution reasonable? What I got from my first attempt is that the time constant won't change. WHY? Because when we double the number of loops (N) we're going to have new values for both the self inductance and the resistance of the solenoid and so the ratio (L/R) stays the same. Here is a...
  10. Abo

    RC time constant problem — confusing problem statement

    Hello! It says that the Time Constant of an RC circuit is equal to 100 ms. What is the energy that remains in the circuit after 300 ms? "Nothing mentioned about whether it is in falling or rising edge". The formulas that I have been using are : W = 0,5 (C* V^2) V = V0 ( e^-t/rc ) since I don't...
  11. paulmdrdo

    Thevenin Resistance and the Time Constant

    Homework Statement Homework Equations Rth = R||R+R (not sure?), τ=Rth*C The Attempt at a Solution [/B] So, what I ultimately wanted to determine is the time constant of this first order op-amp circuit. I first tried to calculate the thevenin resistance seen by the capacitor by using Rth =...
  12. dvscrobe

    Engineering Time Constant of an Opamp Circuit

    Homework Statement : [/B] Find the time constant of an inverting op amp with C = 50uF, Ri = 200 Ohms, Rf = 20 Ohms. This is a problem I have found in a prep book for the Fundamentals of Engineering Exam (Electrical component). The book gives the answer as time constant = Rf * C. I am not...
  13. Shivang kohlii

    Time constant for parallel RC circuit

    Homework Statement Question 6. Homework Equations Time constant = RC The Attempt at a Solution I think answer should be 1/2 RC as Rnet = 1/2R and to convert it to single resistance form we should first find Rnet But the answer is coming out to be RC . How? << Corrected Image added by...
  14. F

    Find the time constant of the circuit

    Homework Statement In the circuit shown S is closed at t = 0 . Find the time constant (in s) if C = 2μF. Homework Equations τ = Req C The Attempt at a Solution R = ##\frac{10*10}{10+10}## R = 5MΩ τ = 5*106 * 2*10-6 = 10 s Could somebody check my answer?
  15. J

    Time constant of an inductor coil

    Homework Statement Homework EquationsThe Attempt at a Solution I think I can solve this problem . But I am bit unsure about how current changes in the circuit and the coil when it is shorted . Before the coil is shorted , there will be no induced EMF across the terminals of the coil ...
  16. G

    Engineering Inductor circuit time constant

    Homework Statement Hi. I started studying LR circuits and the first thing that made me do searches in textbooks of mine and in the internet was the time constant which is surprisingly not L times R, but L/R which would mean the time needed to store and release energy is being prolonged with...
  17. J

    New time constant to change damping ratio

    Homework Statement Homework Equations Time constant = 1/ξwn The Attempt at a Solution Time constant = 1/ξwn Damping factor = ξwn So T = 1/ξwn If ξwn is reduced by factor of 2, then Time constant must be increased by factor of 2. So Answer is: B Book answer is A How? p.s. I know I'm posting...
  18. J

    Time constant of a transfer function

    Homework Statement Homework Equations Express denominator as 1 + sT1 The Attempt at a Solution In denominator s+2 can be written as : 2(1 + 0.5s) s + 3 can be written as: 3(1 + 0.3s) So I have two time constants. Should I multiply them to get final time constant? There is another formula...
  19. J

    Engineering Time Constant for RLC circuit

    Homework Statement Homework Equations I know for RL circuit T = L/R For RC circuit it is RC But how to go ahead for RLC circuit.The Attempt at a Solution I calculated for RL as 1/4 = 0.25 And RC as 1 Then I added both time constant and got 1.25 Book answer is 0.5. How to solve this? In...
  20. H

    Capacitor circuit time constant problem

    Homework Statement How long does it take in time constants ( = RC) for the charge on the capacitor in the circuit shown below to reach one quarter its initial value? Homework Equations C=Q/V time constant=RC Vc = Vo * (e)^(-t/RC) The Attempt at a Solution From C=Q/V I get Q=VC so for the...
  21. N

    Capacitors in series or in parallel? - calculating CR

    Homework Statement I have the circuit above. When I have the switch at A, the capacitor C1 is charging at 100μF is at 10V. I then discharge the capacitor by connecting the switch to B. I was asked to calculate the time constant. I thought the capacitors were in parallel but according to...
  22. W

    Electrophysiology Quick Homework Problems

    Homework Statement Hi guys, I've been trying to solve these two questions for the last hour and can't seem to find the solution, any help would be very much appreciated. :smile: 1. An RC circuit is given a step voltage (charging) of V at t = 0 seconds. What is the value of voltage at t = 2RC...
  23. solour

    Current Through A Resistor That Is In Parallel With A Capacitor

    Homework Statement [/B] My question is regarding part C of the question. Homework Equations V = IR V(t) = V(1-e^(-t/tau)) The Attempt at a Solution My idea is to use Kirchoff's Voltage Law and find the voltage of the capacitor as a function of time, then since the voltage across capacitor is...
  24. A

    Opamp RC-circuit -- Capacitor time constant calculation

    Homework Statement for the opamp circuit give in the figure, find Vo(t) for t > 0 the figure is attached. Homework Equations I know that tau = R * C that is the time constant of a capacitor discharging is equal to the product of the resistor that it discharges through and its capacitance.The...
  25. O

    Engineering What is the time constant in an LC circuit.

    Homework Statement I wrote an exam today and a question worth quite a bit of points asked Determine the value of a capacitor in a series circuit that will give a time constant of 4.0 ms and is isn series with an inductance of 3mH Homework EquationsThe Attempt at a Solution I do not believe...
  26. RoboNerd

    Figuring out why experimental results are different

    Homework Statement Hello everyone, I am trying to figure out how to approach part c, parts i and ii Homework Equations OK. I know that we have the current equation in milliamps as shown above The Attempt at a Solution My problem is giving one possible explanation for the finding and...
  27. sammyqw

    Adding resistance in parallel

    Homework Statement Find total Resistance Homework Equations 1/Req= (1/R1)+(1/R2)... The Attempt at a Solution Can someone please explain me how 5 ohm R and 3ohm R are in series and then in parallel with the 2ohm R? Thanks
  28. H

    Time constant and capacitors

    So the rate at which a capacitor charges and discharges is dependent on resistance in a circuit and the magnitude of capacitance of the capacitor? So the time constant is equal to RC. So using this equation where Q=Qoe-t/RC ,time constant is the time taken (when the capacitor is discharging)...
  29. K

    Determining Thevenin equivalent and time constant

    Homework Statement Homework Equations ; 3. The Attempt at a Solution [/B] Here is my thought process and assumptions. Without Vs1 and R2, the open-circuit current would be Vs2/R2, but I know Vs1 and R1 must be contributing in some way. I'm thinking of summing the Voltage sources and using...
  30. R

    Time for capacitor charging in RLC circuit.

    Homework Statement In series RLC circuit how much time it takes for capacitor to charge to 0.63% of source voltage..? time constant is the time taken by a capacitor to charge to 0.63% of source voltage and in rc circuit time constant is RC. but what about for capacitor in series RLC circuit...
  31. G

    Circuit with a switch

    For the circuit shown in the figure, the switch S is suddenly closed with the capacitor uncharged. After one time constant, the charge on the capacitor is closest to: a) 2.0 mC b) 0.74 mC c) 1.0 mC d) 1.3 mC e) 0.00 mCRelevant Formulas q = Q⋅(1-e-τ/R⋅C) τ = RC My Attempt q = Q(1-e-τ/T) q =...
  32. V

    Time Constant ≠ Time constant from experiment

    Homework Statement Hello, In a lab experiment, we wanted to compare the time constant in a simple RC circuit by comparing the value of Resistance * Capacitance that we measure directly and the value of RC that we get from the procedure. The procedure entailed using a wave generator and an...
  33. K

    A gong that makes damped oscillation

    Homework Statement A gong makes a loud noise when struck. The noise gradually gets less and less loud until it fades below the sensitivity of the human ear. The simplest model of how the gong produces the sound we hear treats the gong as a damped harmonic oscillator. The tone we hear is related...
  34. T

    How do you work out wave envelopes and asymmetries?

    Hi Say I took one or all of the four waves here: How would I go about working out the envelope around their peaks, or finding the exponential time constant from start to steady state? Cheers!
  35. J

    Significance of RC time constant

    In a simple series RC circuit, when t=RC, the voltage across the resistor and capacitor is the same. Why is this physically significant and why do we choose this as the time constant that dictates the cutoff frequency?
  36. Rath123

    Calculating Time Constant in Parallel Plates: Keeping the Capacitor Constant

    How can a time constant, in parallel plates, be the original value without changing the capacitor?
  37. AdityaDev

    Charging of resistor with resistance in parallel

    The cell can provide conatant emf ε and initial charge of capacitor is zero. Now current through resistor initially is zero and increases. But the potential difference across the capacitor is always a constant with magnitude ε. then ##\frac{q(t)}{C}=E## So ##q(t)=CE## which implies q is constant...
  38. R

    Capacitive Time Constant

    Homework Statement A 8500 Ω resistor is joined in series with a 80 μF capacitor. a) What is the capacitive time constant of this combination? (Solved: 0.65 s) b) If a 9.0 volt battery is suddenly connected across this RC combination, how long will it take for the capacitor voltage to reach 8.0...
  39. D

    Charge-Sensitivity in Preamplifier

    How I tell if a preamplifier is charge sensitive? I have data taken from a preamplifier that is fed a pulse from a voltage pulser that is fed through a current generator. As the pulse voltage was increased the preamp output voltage increased linearly. As the pulse width was increase the preamp...
  40. ranju

    Time constant of inductors in machines

    We know that all machines or devices working on AC have high value of time constant so that there is n damage to inductor while current reversal & high value of time constant means increase in time to reach steady state as we can see in fans , coolers , etc. but the tube-lights also have a...
  41. J

    Response time of a magnetic circuit and its elements

    This one is for people working with electromagnets (more specific, DC) etc. I have a few questions that I am struggling with: I am quite comfortable with the concept of the response time (time constant) of a coil in free space, μ0 =4π x 10-7 . The thing I am struggling with is the response time...
  42. A

    Time constant -- How to find the time constant of any given circuit?

    How to find the time constant of any given circuit?? why we don't define time constant for rlc circuit?
  43. I

    Engineering Time constant in RL circuit

    Homework Statement Homework Equations τ = L/R The Attempt at a Solution So I already know the initial current and final current (-4mA and -1mA, respectively), my question is how I would find the resistance value to use to solve for the time constant. After the switch has been closed for a...
  44. ilovescience85

    Inductance, volt drop and time constant? Help

    Good evening all, I am looking for some clarity on a question I am answering at the moment. An inductor of negligible resistance and an inductance of 0.2H is connected in series with a 330ohm resistor to a 12v d.c. Supply determine: A - the time constant of the circuit B - the voltage...
  45. W

    Time Constant Induction question

    Hi all, I need your help with a Time constant question? I am studying for an exam via distance learning and don't feel they have covered this question, question taken from past paper. 2. A coil of inductance 2 H and unknown resistance is connected to a D.C. supply of 100 volts. After 4 ms the...
  46. U

    Find Time Constant for RC Circuit: Solve the Equation!

    Homework Statement The time constant of charging for the capacitor shown in the figure is Homework Equations See attached diagram The Attempt at a Solution \tau = R_{eq} C R_{eq} = R/2 So the answer should be t= RC/2. But the correct answer is 0! :confused:
  47. R

    Find resistance, inductance, and the time constant for an RL circuit.

    Homework Statement A 5.0V battery is attached to an RL circuit. The current is given by the formula: I = V0/R(1-e-t/τ), where I0 is the steady-state current, and τ is the time constant for the circuit. Using the data table provided, determine τ, R, and L for this circuit. I(mA) | t(μs)...
  48. D

    MHB What is meant by find the time constant?

    I solved a DE for an electrical circuit where the input was a step input. \[ \mathcal{U}(t) = \begin{cases} 0, & \text{if } t <0\\ V, & \text{otherwise} \end{cases} \] So the solved DE for \(t > 0\) is \[ q(t) = VC + Ae^{\frac{-R}{C}t}. \] How do I find the time constant? Also, \(q(t)\) is the...
  49. H

    Electrical Science - LR Time Constant & Voltage Drops

    Electrical Science -- LR Time Constant & Voltage Drops 1. An inductor of negligible resistance and an inductance of 0.2 H is connected in series with a 330 Ω resistor to a 12V d.c. supply. Determine: (a) the time constant of the circuit (b) the voltage drop across the inductor after two...
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