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RL Circuits Revision Notes

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16.12RL Circuits


In these revision notes for RL Circuits, we cover the following key points:

  • What are RL circuits?
  • What do RL circuits have in common with RC circuits?
  • How does the current changes in RL circuits?
  • What happens to the voltages in each component of a RL circuit?
  • How to calculate the current flowing at any instant through a RL circuit?
  • What is the inductive time constant?
  • How to find the time in which the current in a RC circuit reaches a given faction of initial or maximum current?

RL Circuits Revision Notes

A RL circuit contains at least one resistor and one solenoid along with other useful components. In other words, in RL circuits, at least one resistor and one inductor are connected in the same wire.

Inductor is one of the major passive components in electronics. The basic passive components in electronics are resistors, capacitors, inductors and transformers.

RL circuits are similar in concept to RC circuits. However, capacitors and inductors have different construction properties, limitations and usage.

A rise or a fall of the current through a RL circuit occurs when a source by an electromotive force ε supplies a single loop circuit containing a resistor R and an inductor L.

From the Kirchhoff's Second Law (the voltage law), which is based on the law of conservation of energy, we have:

ε + ∆V + εi = 0

Or

ε-i ∙ R - L ∙ di/dt = 0

The rise in current in a RL circuit as a function of time t, is:

i(t) = ε/R ∙ (1 - e-t/τL)

while the current fall in such circuits after the switch turns OFF, is

i(t) = ε/R ∙ e-t/τL

where

τL = L/R

is known as the inductive time constant. It has the unit of time (second).

The following rule is applied in the RL circuits:

"An inductor initially opposes the rise in the current in the circuit but after a long time, it acts as a simple conducting wire."

We can apply a logarithmic approach to calculate the time in which the current flowing in the circuit reaches a certain part of the initial or maximum value of current.

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