RL Circuit

An RL circuit is a type of electrical circuit that consists of two key components – a resistor (R) and an inductor (L), connected either in series or parallel with each other. These circuits are used to analyze and control the behavior of current and voltage in an electrical system.

How Does an RL Circuit Work

Resistors are devices that oppose the flow of electric current, and their main function in a circuit is to convert electrical energy into heat. On the other hand, inductors store energy in the form of a magnetic field when current flows through them. This magnetic field generates an opposing force that resists change in the current.

An important aspect of RL circuits is their time-dependent behavior, especially in situations where the current is turned on or off in a DC circuit. The interaction between the resistor and inductor causes the current to rise gradually, and it decays when power is removed by opening the switch. This behavior is governed by the inductance of the coil and the resistance in the circuit.

Transient Response of an RL Circuit

The transient response refers to the circuit’s behavior as it transitions from one steady state to another. It typically occurs when a switch is turned on or off, causing a change in the current and voltage distribution. Unlike purely resistive circuits where current and voltage instantly adjusts to a new steady state, an RL circuit responds gradually due to the inductor’s response to change in current.

Rise of Current

When a constant voltage is suddenly applied to an RL circuit, the inductor initially opposes the flow of current. This opposition is due to Lenz’s Law, which states that the induced electromotive force (emf) in the inductor resists the change in current. As a result, the current in the circuit does not immediately jump to its maximum value. Instead, it rises gradually and slows down as it approaches its final steady-state value.

The equation governing the rise of current over time in a series RL circuit is:

\[ I(t) = \frac{V_0}{R} \left( 1 – e^{-\frac{t}{\tau}} \right) \]

Where:

– t is the time after the voltage is applied

– I(t) is the current at time t

– V₀ is the battery voltage

– R is the resistance

– τ is the time constant of the circuit, defined as τ = L/R

– L is the inductance

Fall of Current

When the power supply to an RL circuit is turned off, the current does not immediately drop to zero. Instead, it decays gradually because the inductor attempts to maintain the current flow. This behavior occurs because the energy stored in the inductor’s magnetic field is released back into the circuit.

The equation governing the decay of current over time is:

\[ I(t) = \frac{V_0}{R} e^{-\frac{t}{\tau}} \]

References
- 1. LR Series Circuit – Electronics-tutorials.ws
  2. RL Circuits – Phys.libretexts.org
  3. RL Circuits – Courses.lumenlearning.com
  4. Understanding RL Circuit Operation and Time Constant – Eepower.com