How do I solve a circuit with multiple nodes and loops?

[tylersmith7690]

Homework Statement

In attatchment

Homework Equations

Not sure How to come up with the other equations.

The Attempt at a Solution

Assuming a node is an element connected to two or more elements.

1) Moving clockwise from V i1 to i2. Node one is between the negative side of the voltage source and first resistor.

2) Node 2 is from first resistor to second resistor on the right and 3rd resistor down the middle.

3) Node 3 is the top right hand corner between those two resistors.

4) node 4 is the entire wire running down from the far right resistor and middle resistor and to the voltage supply.

I also have two loops.
Loop A encompass i2 i7 and i6 and loop B encompasses i3 i4 i5 and the middle resistor.

I'm having trouble setting up the equations as all the references I've looked at have done the questions a little different. Mainly just using the junction method.
current entering = current out.

I have no experience on circuits so this is just what I make of the information I've read.

eq 1 ) using node 1. i1 - i2 = 0
eq 2) using node 2. i2 - i3 - i7 = 0
eq 3) using node 3. i3 - i4 = 0
eq 4) using node 4 i5 + i7 - i6 = 0
eq 5) loop a i2*R + i7*R - V = 0
eq 6) loop b i3*R + i4*R - i7*R = 0

this is where I'm stuck and I'm unsure about my above equations. Is there a outside loop around the entire circuit or is there a node i have missed. I assume i need 7 equations for the 7 unknowns.

Any help would be much appreciated. Kind regards.

 

[Ray Vickson]

Homework Statement

In attatchment

Homework Equations

Not sure How to come up with the other equations.

The Attempt at a Solution

Assuming a node is an element connected to two or more elements.

1) Moving clockwise from V i1 to i2. Node one is between the negative side of the voltage source and first resistor.

2) Node 2 is from first resistor to second resistor on the right and 3rd resistor down the middle.

3) Node 3 is the top right hand corner between those two resistors.

4) node 4 is the entire wire running down from the far right resistor and middle resistor and to the voltage supply.

I also have two loops.
Loop A encompass i2 i7 and i6 and loop B encompasses i3 i4 i5 and the middle resistor.

I'm having trouble setting up the equations as all the references I've looked at have done the questions a little different. Mainly just using the junction method.
current entering = current out.

I have no experience on circuits so this is just what I make of the information I've read.

eq 1 ) using node 1. i1 - i2 = 0
eq 2) using node 2. i2 - i3 - i7 = 0
eq 3) using node 3. i3 - i4 = 0
eq 4) using node 4 i5 + i7 - i6 = 0
eq 5) loop a i2*R + i7*R - V = 0
eq 6) loop b i3*R + i4*R - i7*R = 0

this is where I'm stuck and I'm unsure about my above equations. Is there a outside loop around the entire circuit or is there a node i have missed. I assume i need 7 equations for the 7 unknowns.

Any help would be much appreciated. Kind regards.

Basically, you just have three different currents, i1, i4 and i7. At the top t-junction you have i1 = i4 + i7, and this applies as well at the bottom t-junction (check this!). So that is one equation, and you need two more. Can you see what those other two equations must be?