Energy Dissipation by Inductor (RL circuit)

In summary, the conversation discusses the behavior of an inductor in an RL circuit under different conditions. It is determined that when t < 0, the voltage source has an equation of 40 - 40u(t) and the inductor acts as a short-circuit, causing the current to be 1A. When t > 0, the circuit becomes an RL circuit with a 20 ohms resistor in series with the inductor. The energy dissipated by the inductor is calculated to be 5J and the behavior of the inductor current is described. The conversation also mentions the importance of understanding the behavior of an inductor in DC situations.
  • #1
RiceKernel
17
0

Homework Statement


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Homework Equations


The voltage across an inductor is V(T) = L i'
Basic current division and voltage division .
Step function where u(T) : when t is smaller than 0 : u(t) = 0
t >0 : u(t) = 1

The Attempt at a Solution



The voltage source has the equation 40 - 40u(t).
When t <0 , this means that the value of the VS is 40V.

What happens to the current iL through the inductor...? Does the inductor acts as a short-circuit or open-circuit?
Assuming an Inductor acts as a short-circuit under these conditions, iL= 40V/40ohms =1 Amps

This is my i(0).
Therefore Rth = 20 ohms
t = L/R = 10 / 20 = 1/2

So iL(t) is = 1A(e^(-2t))

When t > 0 , Vin becomes 0 V so the whole circuit becomes an RL circuit which can be simplified using equivalent resistance equation and the final circuit becomes a 20 ohms resistor in series with the inductor.

The energy dissipated by an Inductor is E = (L*i^2) /2 and since we know the initial energy stored in the inductor is (10H( 1A)^2) /2 = 5 Joules,

It must be dissipated by the resistor. So the total energy dissipated by the circuit is 5 J?

The main problem here is with me understand how an inductor behave in this kind of situation (DC I presume). How do we find the initial current and current at infinity? Kind of confused...
 
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  • #2
You have it right. Inductor current starts at 1A and exponentially falls to zero on a time constant involving L and 20 ohms. The stored energy is all lost, so 5J looks correct.

When voltages are steady, the inductor acts like a short circuit.

You might find it instructive to work out what the voltage across the inductor would look like after t=0. Sketch the graph.
 

FAQ: Energy Dissipation by Inductor (RL circuit)

1. What is an inductor and how does it work?

An inductor is a passive electronic component that stores energy in the form of a magnetic field. It is made up of a coil of wire that resists changes in current, and when a current flows through it, a magnetic field is created. This magnetic field then induces a voltage in the coil, which opposes any changes in the current. This property is what allows inductors to dissipate energy.

2. How does an inductor dissipate energy in an RL circuit?

In an RL (resistor-inductor) circuit, an inductor dissipates energy by converting electrical energy into magnetic energy. As the current flows through the inductor, a magnetic field is created, storing energy. When the current stops or changes direction, the magnetic field collapses and releases the stored energy, which is then dissipated as heat in the circuit.

3. What factors affect the rate of energy dissipation in an RL circuit?

The rate of energy dissipation in an RL circuit is affected by several factors, including the inductance of the inductor, the resistance of the circuit, and the frequency of the current. A higher inductance or resistance will result in a slower rate of energy dissipation, while a higher frequency will result in a faster rate of energy dissipation.

4. How is energy dissipation by an inductor measured?

The energy dissipation of an inductor is typically measured in terms of its power dissipation, which is the rate at which energy is dissipated in the form of heat. This can be calculated by multiplying the square of the current flowing through the inductor by its resistance.

5. Are there any applications of energy dissipation by inductors?

Yes, the dissipation of energy by inductors is an important concept in many electronic devices. It is used in power supplies to regulate voltage, in audio equipment to filter out unwanted signals, and in motors and generators to convert electrical energy into mechanical energy. It is also a crucial part of the functioning of electronic components such as transformers and chokes.

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