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The way I understand it is as follows:

Inrush current is the high current drawn by a motor during its acceleration period. Inrush current begins when the motor is turned on and continues until it reaches rated speed. High inrush current decreases as the motor accelerates.

Locked rotor current (LRC) is the highest level of inrush current, which occurs the moment the motor is turned on.

Since at the start of the motor/transformer the transient reactance is very small, where, only the resistance is available, therefore, the inrush current starts very large during which the initial build-up of the magnetic field i.e., charging the inductors increases the electromagnetic coupling and the reactance.

Do you agree?

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  • \$\begingroup\$ You'll need to define what you mean by 'a motor'. Different motors have different sorts of inrush, AC, or DC, permanent magnet or what. Different people will make different assumptions. \$\endgroup\$
    – Neil_UK
    Commented Sep 13, 2021 at 9:46
  • \$\begingroup\$ Locked-rotor current also occurs during a mechanical overload or a failure of the driven system that causes the rotor to stop. This is important for motor protection, since the current must be allowed to flow on a transient basis during startup, but must be interrupted when it flows for too long. \$\endgroup\$
    – Theodore
    Commented Sep 13, 2021 at 15:00

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It's a bit more complex than that I believe.

Magnetic components

Inrush current on AC motors is not the current taken by a motor to accelerate it up to speed but, the current that saturates the magnetic core. This current produces a power/heat that is not redeemable.

For a DC motor the stalled situation at start-up produces large \$I^2 R\$ losses in the rotor resistance that rapidly disappear upon rotation beginning. That stalled situation can be regarded as an "inrush" case.

Current that is taken in order to accelerate a motor to speed is "proper" load current in that it "converts" to rotational energy and is redeemable.

Other notable problematic components are transformers. They can suffer from high inrush currents due to core saturation for the first several cycles of AC. If the supply voltage is activated at the peak of the waveform then inrush current is minimized.

Capacitor charging

Capacitors take a surge current if the voltage is applied abruptly and, because of this, 50% of the potential charging energy is lost as heat so, like magnetic components, there is an irredeemable power or energy loss associated with inrush current.

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Locked-rotor current would be the same as the initial value of inrush current for a DC motor. For an AC motor, the locked rotor current is initially the same as inrush current (described by @Andy aks), but it drops somewhat after the saturation effects subside in a few cycles of waveform.

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