How Do You Calculate Current and Energy Decay in a Source-Free RL Circuit?

In summary, the conversation revolves around a problem in a RL circuit analysis involving a resistance of 1 ohm and an inductance of 2H. The problem asks for the calculation of the current and energy remaining in the inductance at specific times. The person is unsure how to approach solving for the energy and asks for clarification on using the formula I L(t) = 2e^-Rt/L. The responder suggests using a formula for the energy stored in an inductor and clarifies the relationship between joules and watts.
  • #1
juicev85
13
0
We just started source free RL circuit analysis in my circuits class (very easy).
However there is a problem in the HW I am not quite sure how to solve.

Problem: The circuit shown consists of a resistance R = 1 ohm and an inductance l = 2H. At t=0, the inductance is storing 100mJ of energy. Calculate (a) i at t=1s (b) the energy remaining in the inductance at t = 2s.

I can easily solve the problems that give an initial current at t = 0s, but i am not sure about the joules. I know joules are watts/second is there some kind of conversion I can perform to get the current so I can use the I L(t) = 2e^-Rt/L formula. This is an easy problem it just comes down to the fact that the prof. didn't mention anything like this in the lecture. So if you guys can give me the tools I am sure I can solve it.
 
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  • #2
There is a formula for the energy stored in an inductor - it depends on L and I. Check that out in your notes or textbook and use it to find the initial current.
 
  • #3
It would help if the circuit was shown.


BTW - joules are watt-seconds, or watts (W, power) = Joules (energy)/second
 

1. What is a source free RL circuit?

A source free RL (resistor-inductor) circuit is a circuit that does not have any external voltage or current sources connected to it. This means that the circuit has no batteries, generators, or power supplies providing energy to it.

2. What is the purpose of studying source free RL circuits?

The study of source free RL circuits helps us understand the behavior of circuits that do not have external sources connected to them. This can be useful in understanding the transient response of circuits and in designing filters and other electronic components.

3. How do you analyze a source free RL circuit?

To analyze a source free RL circuit, you can use the principles of Kirchhoff's laws and Ohm's law. You can also use differential equations to model the behavior of the circuit over time.

4. What is the time constant of a source free RL circuit?

The time constant of a source free RL circuit is the time it takes for the current in the circuit to reach 63.2% of its maximum value. It is calculated by dividing the inductance of the circuit by the resistance.

5. How does the inductor in a source free RL circuit affect the current?

In a source free RL circuit, the inductor stores energy in the form of a magnetic field. As the current in the circuit changes, the inductor resists this change by inducing a voltage that opposes the change. This can cause the current to decrease over time in the absence of an external source.

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