Finding Resistance in an RL Circuit for Time Constant Calculation

In summary, the conversation discusses a circuit with a switch, inductor, and various resistors. The question is how to find the resistance value to use in the time constant equation. It is determined that the Thévenin equivalent resistance of the circuit to the right of the inductor should be used. The inductor bypasses all of the 50k resistor's current only in the steady state, not while current is varying, so it does not have all its current taken by the inductor during the time of interest.
  • #1
izelkay
115
3

Homework Statement


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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 very long time, the 200mH inductor will become a short circuit, and the current from the 75 V source will bypass the 50kΩ resistor (because it will look for the path with least resistance) after traveling through the 75kΩ resistor and go through the short circuit from the inductor, and then the short circuit from the switch being closed. What would then be the resistance for the time constant equation?
 
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  • #2
After the switch closes, the inductor current time constant involves the Thévenin equivalent resistance of the circuit to the right of the inductor.
 
  • #3
So even though the current bypasses the 50k Ω resistor, the R I would use would still be 75k // 50k?

Or, would it be better to say that after doing the source transformation, the current bypasses both the 50k AND 75k resistor, and still have 50k // 75k as the R value?
 
  • #4
The inductor bypasses all of the 50k resistor's current only in the steady state, not while current is varying. So, no, the 50k does not have all its current taken by the inductor during the time it is of interest to us in this exercise.
 
  • #5
Okay I see, thank you.
 

FAQ: Finding Resistance in an RL Circuit for Time Constant Calculation

1. What is the time constant in an RL circuit?

The time constant in an RL circuit is the amount of time it takes for the current in the circuit to reach 63.2% of its maximum value after a change in voltage.

2. How is the time constant calculated in an RL circuit?

The time constant (τ) can be calculated by taking the inductance (L) in henries and dividing it by the resistance (R) in ohms. This can be represented by the formula τ = L/R.

3. What is the significance of the time constant in an RL circuit?

The time constant is an important factor in understanding the behavior of an RL circuit. It determines the rate at which the current changes in the circuit and how quickly the circuit reaches a steady state after a change in voltage. It is also used to calculate the time it takes for the current to reach certain percentages of its maximum value.

4. How does the time constant change if the resistance or inductance is increased in an RL circuit?

If the resistance (R) in an RL circuit is increased, the time constant (τ) will also increase. On the other hand, if the inductance (L) is increased, the time constant will also increase. This is because a higher resistance or inductance will slow down the rate at which the current changes in the circuit.

5. Can the time constant be used to calculate the energy stored in an inductor?

Yes, the time constant can be used to calculate the energy stored in an inductor. The formula for calculating the energy stored in an inductor is E = 1/2 * L * I^2, where L is the inductance in henries and I is the current in amperes. By rearranging this formula, we can see that the energy stored in an inductor is directly proportional to the square of the current and the inductance. Therefore, the time constant, which is determined by the inductance, can be used to calculate the energy stored in an inductor.

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