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What is the relationship between the inductance and the induced voltage in an RL circuit?

1 Answer

In an RL circuit (a circuit consisting of a resistor and an inductor), the relationship between inductance and the induced voltage is governed by Faraday's law of electromagnetic induction. According to this law, the induced voltage in an inductor is directly proportional to the rate of change of current flowing through it.

Mathematically, the induced voltage (voltage across the inductor) can be expressed as:


induced
=


d

d

V
induced
    ​

=−L
dt
dI
    ​


where:


induced
V
induced
    ​

 is the induced voltage across the inductor (in volts, V).

L is the inductance of the inductor (in henries, H).
d

d

dt
dI
    ​

 is the rate of change of current with respect to time (in amperes per second, A/s).

Key points to note:

The negative sign in the equation indicates that the induced voltage opposes the change in current. In other words, it creates a "back-EMF" that tends to resist the change in current flow.
The larger the inductance (

L), the greater the induced voltage for a given rate of change of current (
d

d

dt
dI
    ​

).
If the current is changing at a constant rate (i.e., a constant value for
d

d

dt
dI
    ​

), the induced voltage will remain constant as well.
If the current is not changing (i.e.,
d

d

=
0
dt
dI
    ​

=0), there will be no induced voltage.

This relationship between inductance and induced voltage is fundamental in understanding the behavior of RL circuits and is essential in various electrical and electronic applications, such as transformers, motors, and generators.
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