When talking about motor circuits, the power circuit switches high current devices and the control circuit switches low current devices. Smaller components and wiring are usually used in the control side as opposed to the power circuit.
How They Work

Look at this schematic diagram of an electrical motor installation, you can see that on the right hand side of the image the control is drawn. It is using a 2 amp circuit breaker (CCB1) as its circuit protection. There is a push button (start), a contactor coil (K1) and an overload fault contact (O/L1) as well.
The circuit takes voltage from L1 on the power circuit and uses that as its supply. The main job of the circuit is to control the contactor (K1) coil, when the start button is pressed the coil will energise and close the (K1) contacts in the power circuit. This will ultimately send power to the motor.
In the power circuit there are larger components and cables due to the fact that its main job is to handle the power that goes to the motor. Isolators, contacts and circuit protection all need to be big enough to handle the motor current in this side of the circuit.
To Recap:
The control is responsible for switching small current devices that then in turn switch larger current devices in the power circuit.
Learn more
Fundamentals of Electrical Controls
3 Phase Motor Control Bootcamp
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