Is a blowout coil connected in series with the line of a motor?
No. A blowout coil is used in a switching device to extinguish or "blow out" the arc produced when contacts make or break.
IT IS IN SERIES WITH THE STATIONARY CONTACT OF THE RELAY OR CONTACTOR. IF IT IS THE "M" CONTACTOR IF A DC MOTOR IT IS IN SERIES WITH A1, AND CAN BE OPEN.