Furnace circuit breaker fried

You need to use rated breaker and did you find a fault for why the breaker shorted?

In a traditional North American residential electrical panel (120/240 volt, single phase), installing a single width or single pole circuit breaker, you would expect to read 120 volts from the breaker terminal screw to either ground or neutral. A double width or double pole breaker would provide 120 volts from either of the breaker terminal screws to ground or neutral AND it will provide 240 volts BETWEEN the TWO breaker terminals.

A single-width circuit breaker case that contains two handles is NOT a two pole circuit breaker (these are called "tandem" or "1/2 size" breakers). This is because a single width breaker engages only one "line" in the panel. A double width breaker will engage 2 "lines" as a triple width breaker would engage 3 "lines" of a 3 phase panel. A single wide breaker can not physically engage more than 1 "line" so it will never be able to pass 240 volts.

You must install a double width / double pole breaker to safely supply a 240 volt circuit / device.

200 Amp Double-Pole 10kA Type QPP Circuit Breaker home depot

You need 240 breaker:
Notice that your 240V breaker is twice as wide as regular 120V breaker.
Notice that both switches are tied together on 240V breaker, making this a double-pole breaker.
For more information about breakers and 120-240V circuits:
http://waterheatertimer.org/See-inside-main-breaker-box.html
http://waterheatertimer.org/B220C.html

There should be a disconnect or switch at the furnace, otherwise you'll have to go to the Main circuit breaker or fuse panel and hope the circuits are identified correctly and turn OFF the circuit breaker or unscrew the fuse. If the panel isn't labeled, just turn OFF the single pole breakers until the furnace turns OFF.

Most two-pole breakers have a small plastic bar that connects the two switches allowing them to be synchronized and used as a single breaker. However there are some two pole breakers that are intended to be used as two separate breaker and lack the need for the bar that synchronizes them, this is because they are not being used to power a single circuit or item, but separate circuits, or items. so no the breaker is not bad, and yes can be used to power single circuits or items.

The breaker is bad and needs to be replaced when they do that.

You need to get a new electrician; a real electrician would read the power requirements on the motor name plate and install the correct voltage and amperage circuit.

A single pole breaker does not supply the same voltage as a double pole breaker. It hums because the voltage is wrong

It sounds like this circuit breaker is worn out and needs to be replaced. good luck

this is a double pole circuit breaker that is used for a 240 volt device the bar in the middle is to shut down at the same time you can take it to a hardware store to replace it but the bar is factory made siemens is one common breaker or there might be a substute they can give you also