Natural response RL circuit

In summary, the conversation discusses the derivation of equations for i(t) and v(t) in two different circuits, A and B. In circuit A, the passive sign convention is used for the inductor, resulting in exponential decay for both i(t) and v(t). In circuit B, the voltage induced across the inductor is opposite to the change in current, leading to growth equations for both i(t) and v(t). The question of why the signs are different between the two circuits is raised, and the speaker mentions a potential sign error in the "physics" version of the equation. The conversation also touches on the expectation of the same graph for both i(t) and v(t) in circuit A. The final value of
  • #1
paulmdrdo
89
2
as you can see In the image I provided I have derived the equation for i(t) and v(t).

On circuit A I use a passive sign convention(current flowing from positive to negative) on the inductor, hence the equation and their corresponding graph.
i(t) is decaying exponentially, v(t) is decaying exponentially.

On circuit B I did use what I learned in physics, i.e the voltage induced across an inductor is always opposite to the increase/decrease in current
flowing throuhg it. Since the current i(t) is decreasing, the voltage should support that current hence the sign. when I perform kvl on circuit B I ended up having growth equation for both i(t) and v(t). Why is that?

Also in circuit A I expect to have same graph for both i(t) and v(t) (Although they are both decaying).
Please, kindly clear this up for me if you have time. Thanks!
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  • #2
What is the final value of the current through the inductor (when the current does not vary any longer)?
 
  • #3
The signs are not consistent between the two circuits therefore you can't use v=Ldi/dt (using the symbols from the schematics) in both algebraic solutions. i.e. circuit a has positive current entering the + terminal of L. Circuit B has positive current leaving the + terminal of L and this is why it shows current growth.

Edit: I just realized you made the sign error on purpose. The issue is still a sign error. But you dropped it from the "physics" version of the equation. See the link below.
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/induct.html#c1
 
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1. What is a natural response RL circuit?

A natural response RL circuit is a type of electrical circuit that contains a resistor (R) and an inductor (L). When an electrical current is applied to the circuit, the inductor resists the flow of current and causes it to build up. This buildup of current creates a magnetic field, which in turn, produces a voltage that opposes the applied voltage. This opposition to the applied voltage is known as the natural response.

2. How does the natural response of an RL circuit differ from the forced response?

The natural response of an RL circuit is dependent on the properties of the circuit components (resistor and inductor) and does not require an external source to create the response. On the other hand, the forced response is caused by an external voltage or current source that is applied to the circuit. The forced response is superimposed on the natural response and can be controlled by the external source.

3. What factors affect the natural response of an RL circuit?

The natural response of an RL circuit is affected by the values of the resistor and inductor, as well as the initial conditions of the circuit (such as the current and voltage at the start). The time constant of the circuit, which is determined by the product of the resistance and inductance values, also plays a role in the natural response.

4. How is the natural response of an RL circuit mathematically represented?

The natural response of an RL circuit can be mathematically represented by an exponential function, where the current or voltage at any time (t) is equal to the initial value multiplied by the natural exponential function raised to the power of -t divided by the time constant (RC). This can be written as I(t) = I0e-t/RC or V(t) = V0e-t/RC, depending on whether current or voltage is being measured.

5. What are some real-world applications of natural response RL circuits?

RL circuits are commonly used in electronic devices, such as speakers, motors, and generators. They are also used in power transmission systems, where the inductor helps to regulate the flow of current and maintain a stable voltage. Additionally, RL circuits are important in the study of electromagnetic waves and can be found in various communication systems, such as radio and television receivers.

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