Name: rl step response under a dc source
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 14 s
Channel: JoVE

When an RL circuit is connected to a DC source, its complete response is divided into transient and steady-state responses.
The transient response is the circuit&#39;s temporary response that exponentially decays to zero as the time approaches infinity.
The inductor then acts as a short circuit, and the source voltage drops across the resistor.
At this instant, the current in the circuit becomes steady and equals the ratio of the source voltage to resistance. This is the steady-state response.
Substituting the steady state and transient response yields the total response of the RL circuit.
The constant term is determined by substituting the initial current through the inductor at a time equal to zero.
The complete step response, depicted graphically, shows that the initial current exponentially decreases to a steady-state value.
If the initial current is zero, the complete step response shows the exponential increase of current to a steady-state value.
The voltage response exponentially decreases to zero with an initial voltage equal to the source voltage.

rl circuit met bron

Wanneer een RL-circuit (Resistor-Inductor) is aangesloten op een DC-bron, kan de volledige respons van het circuit in twee delen worden verdeeld: de transiënte respons en de stabiele respons. De voorbijgaande respons van het circuit is de tijdelijke reactie op de plotselinge toepassing van de gelijkstroombron. Deze respons wordt gekenmerkt door een stroom die exponentieel afneemt tot nul naarmate de tijd oneindig nadert. Tijdens deze overgangsperiode gedraagt de inductor zich als een kortsluiting, waardoor de bronvoltage over de weerstand daalt. Zodra de transiënte respons tot nul is vervallen, komt het circuit in de stabiele fase terecht. In deze fase wordt de stroom in het circuit stabiel, gelijk aan de verhouding van de bronvoltage tot de weerstand van het circuit. Dit is de steady-state-reactie. De constante term in de transiënte respons kan worden bepaald door de initiële stroom door de inductor te vervangen op het moment dat de schakelaar wordt gesloten (t = 0). Dit geeft ons de initiële voorwaarde voor de voorbijgaande respons. Het uitzetten van de volledige stapresponsie van het circuit laat zien dat de initiële stroom exponentieel afneemt totdat deze een stabiele waarde bereikt. Uit deze stroomrespons wordt de voltagesrespons afgeleid, die ook een exponentieel verval volgt van een maximale waarde naar nul. Als de initiële stroom in het circuit nul is, laat de volledige stapreactie zien dat de stroom exponentieel toeneemt totdat deze de stabiele waarde bereikt. Dienovereenkomstig begint de voltagesrespons bij de bronvoltage en neemt exponentieel af tot nul. Concluderend biedt het begrijpen van de volledige respons van een RL-circuit op een DC-bron waardevolle inzichten in hoe deze circuits reageren op plotselinge veranderingen in de ingangsvoltage. Deze kennis is essentieel voor het ontwerpen en analyseren van elektronische circuits, vooral in toepassingen zoals voedingsfiltering en signaalverwerking, waarbij inductoren op grote schaal worden gebruikt.

RL Circuit met bron

When an RL circuit is connected to a DC source, its complete response is divided into transient and steady-state responses.
The transient response is the ...

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RL Circuit with Source

rl step response under a dc source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied.

During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source voltage drops across the resistor.

The constant term in the transient response comes from the initial inductor current at the moment the switch closes, which is t = 0. That initial value gives the starting condition for the response. As the transient dies out, the circuit reaches steady state.

In steady state, the current becomes stable. Its value equals the source voltage divided by the resistance. The current response can be plotted to show the exponential change toward this final value.

The voltage response is also derived from the current response. When the current decays from an initial value, the voltage drops exponentially from a maximum value to zero. If the initial current is zero, the current instead rises exponentially to the steady-state value, and the voltage starts at the source voltage and falls to zero.

Understanding the complete response of an RL circuit to a DC source helps explain how these circuits react to sudden changes in input voltage. This idea is useful in circuit design and analysis. It is especially important in applications such as power supply filtering and signal processing, where inductors are used extensively.

RL Step Response Under a DC Source

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key terms and concepts

Explore how an RL circuit responds to a DC source, including transient and steady-state behavior, exponential current change, and voltage decay.

RL Step Response Under a DC Source | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

RL Step Response Under a DC Source

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