How do I find the current in this circuit?

[clurt]

< Moderator Note -- thread moved from the EE forum to the Homework Help forums >

Please view the attached.

The answers are:
i1 0.1429
i2 0.4286
i3 0.2857

So how do I work this out? I assume you use kirchhoffs current law, can someone show me the step? Thanks :)

 

[Jony130]

For loop I we can write this KVL
10V - I1*R1 - (I1 + I2)*R3 = 0
And for loop II
20V - I2*R2 - (I2 + I1)*R3 = 0

Solve this for I1 and I2. And from KCL I3 = I1 + I1

http://www.wolframalpha.com/input/?i=10 - I_1*10 - (I_1 + I_2)*40 = 0 , 20 - I_2*20 - (I_2 + I_1)*40 = 0 solve I_1 and I_2

Or we can use nodal analysis.
For node A we can write a KCL
I1 + I2 = I3

I1 = (10V - VA)/R1
I2 = (20V - VA)/R2
I3 = VA/R3

And solve for VA voltage.
http://www.wolframalpha.com/input/?i=(10 - a)/10 + (20 - a)/20 = a/40

 

[clurt]

For loop I we can write this KVL
10V - I1*R1 - (I1 + I2)*R3 = 0
And for loop II
20V - I2*R2 - (I2 + I1)*R3 = 0

Solve this for I1 and I2. And from KCL I3 = I1 + I1

http://www.wolframalpha.com/input/?i=10 - I_1*10 - (I_1 + I_2)*40 = 0 , 20 - I_2*20 - (I_2 + I_1)*40 = 0 solve I_1 and I_2

Or we can use nodal analysis.
For node A we can write a KCL
I1 + I2 = I3

I1 = (10V - VA)/R1
I2 = (20V - VA)/R2
I3 = VA/R3

And solve for VA voltage.
http://www.wolframalpha.com/input/?i=(10 - a)/10 + (20 - a)/20 = a/40

thanks mate