# What is the best way of solving the circuit?

#### THE_RB

Joined Feb 11, 2008
5,438
"Sudoku style". Start by deducing the bits you can do, and that will give you more info on what the other bits are doing.

#### ErnieM

Joined Apr 24, 2011
8,274

Make 4 current loops clockwise. I1 is where marked, then continuing around to the right then up for I2 (thru 24 ohm), I3 (thru 4 ohm) and I4 (thru 20 ohm).

By inspection:

I1 - I3 = 3A

-I2*24 + (I3-I2)*15 = 100V

I3 - I4 = 3*I1

6*I1 + 24*I2 + 4*I3 + 20*I4 = 0

That's 4 equations in 4 unknowns.

• justtrying

#### WBahn

Joined Mar 31, 2012
26,398
I'd say it's a toss up between mesh, node, and ad-hoc. I don't see any obvious source transformations.

If you use nodal analysis, note that there are five nodes. You always get to declare on of them to be 0V. I'd pick the center node. Then you immediately have the bottom node since it is tied to the reference node via a voltage source. So now you only need three equations. Dealing with current sources is easy in nodal analysis, but in this case it is even easier to go ad-hoc noting that you can write equations for the left node in terms of i1 and the bottom node (and the resistor between them). So you only have to do node equations for the other two.

#### mlog

Joined Feb 11, 2012
276
Toss up. Good answer. That's what I thought too. Nothing is obviously simple, or is that simply obvious? Never mind. #### The Electrician

Joined Oct 9, 2007
2,887

Make 4 current loops clockwise. I1 is where marked, then continuing around to the right then up for I2 (thru 24 ohm), I3 (thru 4 ohm) and I4 (thru 20 ohm).

By inspection:

I1 - I3 = 3A

-I2*24 + (I3-I2)*15 = 100V

I3 - I4 = 3*I1

6*I1 + 24*I2 + 4*I3 + 20*I4 = 0

That's 4 equations in 4 unknowns.
The first equation is incorrect; it should be:

I4 - I1 = 3A

• ErnieM

#### panic mode

Joined Oct 10, 2011
2,113
i would start by naming nodes and currents, rest is .... toss up

#### ErnieM

Joined Apr 24, 2011
8,274
The first equation is incorrect; it should be:

I4 - I1 = 3A

Here's how I was defining the loop currents and resistor voltages: The first equation is in error. The constant current source 3A is the combination of I1 and I4. I4 is in the direction of the source, while I1 is in opposite direction. Thus the correct equation should be:

I4 - I1 = 3A

As the Electrician correctly pointed out. While I trust he checked the other equations as thoroughly, it's not *my* assignment, and the ultimate answers calculated should be verified. #### panic mode

Joined Oct 10, 2011
2,113
While I trust he checked the other equations as thoroughly, it's not *my* assignment, and the ultimate answers calculated should be verified. totally agreed 