# Mesh analysis with 3 loops

This one has 3 loops. I need to assign a direction (e.g clockwise), form 3 equations and solve simultaneously. But I can't seem to do this question. There's no voltage source on the third loop. Any help?

First hint refer to diagram below, can you find the voltage drop across R3. If the values of all R and V is given.

Edit : Second hint refer to your original diagram, (I3 - I1)(30) + I3(20) + (I3 - I2)(40) = 0. Refer to diagram below for the direction of the current assumed. Try browsing through this link for better understandings.

Example:

Refer to the picture below if you should get the correct equation by following the steps in the image Image Source

I feel that you are asking a fundamental question in electrical engineering, that's only reason for me not to give you a direct answer or solution instead I'll try my best to guide you to get the solution.

• so i got 3 equations 1) 110i1-50i2+30i3=100 2) -20i1+30i2+40i3=50 3)90i3=0 . getting i1=2.39, i2= 3.26, and i3=0 . can you confirm this . much appreciated thanks . thank u for the hints too Feb 6, 2015 at 2:11
• Sorry my bad, Have edited accordingly. Feb 6, 2015 at 2:14
• thanks very much , makes more sense now . these are the 3 equations i have come up with . do they seem correct? 1) 110i1-50i2+30i3=100 2) -20i1+30i2+40i3=50 3) -30i1-40i2+90i3=0 ?thanks again Feb 6, 2015 at 2:35
• Please include your workings by editing the questions, this would allow others to join in and correcting it. Long comments shall be continued in chat room. There is few way to solve this question. I haven't work it out yet. Feb 6, 2015 at 5:36

1: Simple answer: no voltage source in loop - set loop equation to 0. in this loop, some branch voltages will be + and some -.
2: Your 3rd loop eq is wrong - it leaves out the loop currents in the border resistors.
3. In the circuit in one of the answers, R3 is in parallel with the voltage source, so no equation is needed. VR3 = V

Just voltage drops/gains need to be accounted for. you dont need sources.

• This is awfully thin for an answer. Can you elaborate? Feb 6, 2015 at 16:38
• sure. All elements within a circuit will have a voltage drop associated with them. all these drops must sum to 0. this is true regardless of any sources within the local circuit. Feb 18, 2015 at 23:54
• But how are the drops anything but zero if there are no sources? Feb 19, 2015 at 4:16