Time constant for the current through the inductor

In summary, the circuit has a voltage of 6 volts, a resistance of 10 ohms, and an inductance of 100 mH. The time constant for the current through the inductor is found using the equation TAU = 2L / R. The equivalent resistance at the open terminals is R/2, making the time constant 2L/R.
  • #1
syhpui2
28
0

Homework Statement



wjD8Y.png


http://i.imgur.com/wjD8Y.png

In the circuit below, V = 6 volts, R = 10 ohms, L = 100 mH. The switch has been open for a long time. Then, at time t = 0, the switch is closed.



What is the time constant for the current through the inductor?

2L / R


Homework Equations



TAU=l/R

The Attempt at a Solution



I am not sure how do I find the equvialent resistance in this case.
 
Last edited:
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  • #2
Kill the source (short the voltage supply) and remove the inductor. Find the equivalent resistance at the terminals where the inductor was.

attachment.php?attachmentid=40334&stc=1&d=1319604076.gif
 

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  • #3
gneill said:
Kill the source (short the voltage supply) and remove the inductor. Find the equivalent resistance at the terminals where the inductor was.

attachment.php?attachmentid=40334&stc=1&d=1319604076.gif


Equvialent resistance is 2r then time constant should be L/2R?

instead of 2L/R?

Thanks
 
  • #4
syhpui2 said:
Equvialent resistance is 2r then time constant should be L/2R?

instead of 2L/R?

Thanks

Nope. Those two resistors are not in series with respect to the open terminals. So the resistance is R/2. That makes your time constant 2L/R.
 
  • #5


The time constant for the current through the inductor can be calculated using the equation TAU = L / R, where L is the inductance and R is the resistance. In this case, the inductance is given as 100 mH (0.1 H) and the resistance is 10 ohms. Therefore, the time constant can be calculated as 0.1 H / 10 ohms = 0.01 seconds. This means that it will take approximately 0.01 seconds for the current through the inductor to reach 63.2% of its maximum value after the switch is closed. This time constant is important in understanding the behavior of the circuit and can be used to calculate other parameters, such as the rise time of the current.
 

What is the time constant for the current through the inductor?

The time constant for the current through the inductor is a measure of how quickly the current in an inductor will reach its maximum value when a voltage is applied. It is represented by the symbol τ (tau) and is calculated by dividing the inductance of the inductor by its resistance.

Why is the time constant important?

The time constant is important because it determines the rate at which the current in an inductor will change. This has practical implications, as it can affect the performance and efficiency of electronic circuits, particularly in applications such as filtering and timing circuits.

How does the time constant affect the behavior of an inductor?

The time constant affects the behavior of an inductor by determining how quickly the current in the inductor will reach a steady state. It also affects the rate at which the inductor will discharge when the voltage is removed, as well as the frequency response of the inductor in AC circuits.

What factors can affect the time constant of an inductor?

The time constant of an inductor can be affected by several factors, including the inductance and resistance values, the type of material used in the inductor, and the frequency of the input voltage. Additionally, the presence of other components in the circuit can also impact the time constant.

How can the time constant be calculated?

The time constant can be calculated by dividing the inductance of the inductor by its resistance. Alternatively, it can also be calculated by multiplying the inductance by the resistance, as they have the same units (seconds). The value of the time constant can also be determined experimentally by measuring the rise or fall time of the current in the inductor when a voltage is applied or removed.

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