Finding Currents in a Circuit

[theuniverse]

Homework Statement

Find currents I1-I6. I'm really looking only for the equations though...

Homework Equations

V=IR

The Attempt at a Solution

I tried to set up equations for the nodes and loops:
Node a:$$I_2-I_6-I_3=0$$
Node b: $$I_3+I_5-I_1=0$$
Node d: $$I_1-I_4-I_2=0$$

Loop 1: $$-V_1+I_1R_1+V_2+I_5R_2$$
Loop 2: $$-V_2+I_2R_5+I_6R_4$$
Loop 3: $$I_3R_6-I_5R_2-I_6R_4$$

I'm pretty sure that the above equations are not correct since I was not sure how to incorporate R3 and I am also a little bit confused about how to relate I1 and I2 and I4.

Thanks for the help!

 

[gneill]

Your node current equations look fine, except that you seem to have interchanged nodes a and d.

For your loops, they need to be in the form of equations (there should be an "=" in there somewhere). For loop 1, treat R3 as you did the other resistors; there's a voltage drop across R3 due to the loop current i1 flowing through it.

 

[theuniverse]

Yeah I meant to equal all the loops to 0. How about this:
Loop 1: $$-V_1+I_1(R_3+R_1)+V_2+I_5R_2=0$$
And you are right about the nodes a and d.. They are switched in my diagram on paper.. thanks!

 

[gneill]

Yeah I meant to equal all the loops to 0. How about this:
Loop 1: $$-V_1+I_1(R_3+R_1)+V_2+I_5R_2=0$$

Yup. That looks okay.

And you are right about the nodes a and d.. They are switched in my diagram on paper.. thanks!

You're welcome

 

[asteriatic]

Your approach in setting up equations for the nodes and loops is correct. However, there are a few corrections and additions that need to be made.

Firstly, in loop 1 and loop 2, you have not accounted for the voltage drops across resistors R3 and R4 respectively. These should be included in the equations as follows:

Loop 1: -V1 + I1R1 + V2 - I3R3 + I5R2 = 0
Loop 2: -V2 + I2R5 + I6R4 - I3R3 = 0

Additionally, in node a, the equation should include the voltage source V1 as follows:

Node a: I2 - I6 - I3 = V1

Similarly, in node d, the equation should include the voltage source V2 as follows:

Node d: I1 - I4 - I2 = V2

Finally, to relate I1, I2, and I4, you can use the junction rule, which states that the sum of currents entering a node must equal the sum of currents leaving the node. This can be represented in equations as follows:

Node b: I3 + I5 - I1 = 0
Node d: I4 + I2 - I1 = 0

Solving these equations simultaneously will give you the values for I1, I2, and I4. The values for I3, I5, and I6 can then be calculated using the equations you have set up for the nodes and loops.

I hope this helps clarify your approach. Good luck with your calculations!