electronic solonoid change/repair
TRIAC replacement

If you have one of the newer KENMORE canister vacuums with a power brush, you have an electronic component controlling the main vacuum motor.
It consists of a circuit board in the main vacuum  which recieves a low amperage signal from the hose switch to turn on the higher amperage motor.
In the past it was a beefy mechanical switch/solonoid, now it is a pittiful fragile (and expensive) little circuit board.
If you want to repair the circuit board you need to find an electronics store that sells small components. You probably need a triac.
A TRIAC has 3 terminals, m1   m2  and gate.  It is A/C so the polarity doesn't matter. The gate (yellow) has 2 resistors and a diac in line (for phase control) and a capacitor across the blue an yellow.
The TRIAC  functions as a switch to turn on the main vacuum motor. The red and blue wires are the switch wires, the yellow is the trigger, or gate that supplies a small amount of current to trigger the switch to close. From SEARS the board costs over $60.00    solder  in the TRIAC yourself- about $2.50