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.

 

[sardar]

I can explain the concept of voltage across resistors in series and parallel in a simple way. In a series circuit, the voltage across each resistor is equal because the current flowing through each resistor is the same. This is because in a series circuit, the current has only one path to flow through, so it must be the same at any point in the circuit.

On the other hand, in a parallel circuit, the voltage across each resistor is not equal because the current is divided among the different paths. This means that the total current flowing into the circuit is divided among the resistors, but the voltage remains the same across each resistor. Therefore, in the given circuit, the voltage across bulb B and the 10 ohm resistor is the same because they are in parallel and have the same current flowing through them.

You are correct in stating that V=IR, but this equation applies to individual resistors, not the entire circuit. In a series circuit, the voltage across the entire circuit is equal to the sum of the voltages across each resistor. In a parallel circuit, the voltage across the entire circuit is equal to the voltage across each individual resistor.

I hope this explanation helps to clarify the concept for you. If you have any further questions, please do not hesitate to ask.