Voltage across resistors in series and parallel

[TrolliOlli]

So I must be missing some crucial knowledge in my knowledge of electrostatics because I simply don't understand how this works. I'm given a circuit like this:

[PLAIN]http://img3.imageshack.us/img3/8730/circuiti.png

and I find out the voltage across bulb B is the same as that across the 10 ohm resistor.

I was under the impression that, since we know V = IR and we know the current across B is the same as the current across the 10 ohm resistor the Voltage would be different assuming B has a resistance other than 10 ohms. What am I missing here?

 

[Doc Al]

The voltage is the same, not necessarily the current. Branches in parallel have the same voltage.

 

[TrolliOlli]

The voltage is the same, not necessarily the current. Branches in parallel have the same voltage.

Would that also apply to two resistors in series? If I simply had a battery with two resistors in series would their voltage be equal regardless of whether or not their resistors were equal?

 

[Doc Al]

Would that also apply to two resistors in series? If I simply had a battery with two resistors in series would their voltage be equal regardless of whether or not their resistors were equal?

Things in parallel have the same voltage; things in series have the same current.