Solving Combined circuit question

[NeomiXD]

I've attached a conbined circuit diagram to this post. I have to solve the circuit. I know that I have to simplify the diagram into a series circuit to make it easier to solve, but I'm having trouble with a few parts in the diagram.

This is how I simplified so far:

1. I added R₆ and R₅ together using the series formula. I labeled it R₈.

2. I added R₄ and R₈ together using the parallel formula. I labeled it R₉.

3. I added R₁, R₂ and R₃ together using the parallel formula. I labeled it R₁₀.

This is where I'm having difficulty. Do I add R₇ and R₉ (from step 2) together using the series formula or do I leave it the way it is.

 

[gneill]

This is where I'm having difficulty. Do I add R₇ and R₉ (from step 2) together using the series formula or do I leave it the way it is.

It looks as though you can add R7 + R9 + R10. They are all in series.

What you add when really depends upon what it is you're ultimately trying to solve for. If it's just the total current that the battery will be producing, then by all means reduce everything to a single resistance!

 

[NeomiXD]

I actually have to find the following:

RT = ?
IT = ?
I1 =?
I3 =?
I6 =?
I4 = ?
V2 = ?
V5 = ?
V7 = ?

I tried solving by adding R7 and R9 (from step 2) together using the series formula. I only had to find 2 more values (V7 and I7)but then I had difficulty figuring out how to find the value of V7 and I7 when only R7 was available.

 

[gneill]

The current through R7 must be equal to the total current, since it is a series circuit and it is a series component of that circuit. Use Ohm's law to work out the voltage across it given the current through it.

You can always "undo" any of your combinations to get at the individual components. For example, once you solve for the total current, you know that it flows through R7, R9, and R10. Therefore you can determine the voltages across each of those resistances. Now, R10 is really three resistors in parallel. So you now have the voltage that is across each of them (parallel resistors all have the same voltage across them). So you can use Ohm's law to determine the individual currents for each of the three resistors (these currents should add up to the total current).