# What is the time constant in an LC circuit.

• Engineering
• OmniNewton
In summary, the question was misleading and confusing. The answer was just the period of this circuit.
OmniNewton

## 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

## The Attempt at a Solution

I do not believe there is a time constant since the circuit is in natural response so therefore this voids the problem

Last edited:
Could it be asking for the period of oscillation?

Sorry let me update the description exactly, The question was: Determine the value of a capacitor in a series circuit that will give a time constant of 4.0 ms and is in series with an inductance of 3mH. I thought about the period of oscillation but it particularly said time constant. They are very strict and won't let you ask anything.
My thoughts were it was a trick question

I think it would be true to say that any expression comprising circuit constants and which has units of time (e.g., seconds) can be termed a time constant.

The reciprocal of seconds is written s–1 and can be pronounced "Hertz".

The question is misleading and confusing. A time constant is associated with an exponential rise or decay, which is not the case here. A period is not a time constant in electrical parlance.

rude man - yes, in general I do support your view .
However, in this case, I am inclined to say that the ENVELOPE of the decaying sinusoidal step response (exponential envelope function) could be the answer (most probably)

LvW said:
I am inclined to say that the ENVELOPE of the decaying sinusoidal step response (exponential envelope function) could be the answer (most probably)
Doesn't that sound too easy, given that the circuit presented is lossless? Especially when ...
The OP said:
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
In exams, be guided by the number of marks awarded.

No examiner gives marks for a candidate stamping his feet and complaining that a question is not well-phrased. The examiner has a particular answer in mind, and marks are awarded according to how well candidates manage to divine his answer from the clues he casts about.

So the exam was returned and the answer was just the period of this circuit. However since the question can perhaps create confusion everyone was given full credit on the problem.

NascentOxygen

## 1. What is an LC circuit?

An LC circuit is an electrical circuit consisting of an inductor (L) and a capacitor (C) connected in series or parallel. It is a type of resonant circuit that can store and release energy at a particular frequency.

## 2. What is the time constant in an LC circuit?

The time constant in an LC circuit is the time it takes for the energy stored in the capacitor to decrease by a factor of 1/e (approximately 36.8%) when the circuit is opened or the power source is removed. It is denoted by the symbol τ and is equal to the product of the inductance (L) and capacitance (C) in the circuit.

## 3. How is the time constant calculated in an LC circuit?

The time constant (τ) in an LC circuit can be calculated using the formula τ = L/C, where L is the inductance in henries and C is the capacitance in farads.

## 4. What is the significance of the time constant in an LC circuit?

The time constant is an important parameter in an LC circuit as it determines the rate at which the energy stored in the capacitor will dissipate once the circuit is opened or the power source is removed. It also affects the frequency at which the circuit will resonate and the overall behavior of the circuit.

## 5. How does the time constant affect the behavior of an LC circuit?

The time constant in an LC circuit affects the speed at which the energy is transferred between the inductor and capacitor, which in turn affects the resonant frequency and the bandwidth of the circuit. A shorter time constant results in a higher resonant frequency and a narrower bandwidth, while a longer time constant results in a lower resonant frequency and a wider bandwidth.

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