Voltage divider rule simple question

[orangeincup]

Homework Statement

See picture.

Homework Equations

i=v/R
v*(r1/(r1+r2))

The Attempt at a Solution

My question is about the solution in the picture. According to the solution, v*8/(8+16) and v*8/(4+8) equal both respective sides of the circuit A and B. My question is, why is this true? Why couldn't you take v*4/(8+16) and v*8/(4+8) for example? Why does it have to be like they wrote it? I thought the voltage divider rule was to find the voltage between two parallel resistors, but in this case it seems to be finding the voltage in two parallel resistors independently? I didn't think this was possible.

Also, is the 4 and 8 on the right side parallel or in series? Does the 1 ohm resistor make them in parallel? I assume it does. Why wouldn't the solution be something like...

for a)

V*(8||16)/((8||16+(4||8))?

 

[ehild]

Also, is the 4 and 8 on the right side parallel or in series? Does the 1 ohm resistor make them in parallel? I assume it does.

No, they are in series, just like the resistors on the left. The 1 ohm resistors do not count as one of their terminals are not connected to anywhere. Therefore no current flows though them.

You need to determine the potential difference between points A and B. For that, you need the potentials with respect to a common point where you set the potential to zero. It is the line at the bottom of the circuit, which is connected to the negative terminal of the battery.
There is no current flowing through the 1 ohm resistors, so the potential at A is the same as the common point of the 16 ohm and 8 ohm resistors, and they can be considered connected in series. The same with the chain of the 4 ohm and 8 ohm resistors on the right.

The upper end of both chains of resistors are connected to the positive terminal of the battery, so the potential difference is 12 V across them.
You can calculate the currents flowing in both chains, and knowing the currents, you know the voltages across the 8 ohm resistors in both chains.

ehild

 

[andrevdh]

There is no current in the one ohm resistors, so there is no potential drop over them.
So you can ignore them. The problem is then in effect to find the potential difference
between the two points in the middle of the two resistors on the left and the two on the right.
There are two branches for the current one on the left and one on the right and
these two branches are running in parallel so that the voltage over these two branches
will be the same, 12V.