I can’t figure out this circuit. How to obtain the three currents

circuit analysis

I can't figure out why i2 is 0. I tried applying KVL on the mesh with the voltage source but I didn't get anywhere (perhaps I applied it incorrectly? i don't know if the current travelling through that mesh is i2 or not). I also don't know how to obtain i1 and i0 once I obtain i2. (i'm guessing the voltage is the same on the 2 and 5 resistors? but i could be wrong). A little help would be greatly appreciated.

Best Answer

Thanks everyone for helping me figure it out! \$i_2\$ has to be 0 because it has no loop to go through.

So I solved the left hand side and right hand side separately and I got these results:

\$V_{\Delta} = \dfrac{10}{10 + 2} \times 24 = 20 V\$ (voltage divider)

So the current source is \$0.8 \times V_{\Delta} = 16 A\$

Then I used a current divider to get \$i_1\$ and \$i_0\$.

\$i_1 = \dfrac{5}{20 + 5} \times ( -16 ) = -3.2 A\$

\$i_0 = \dfrac{20}{20 + 5} \times ( -16 ) = -12.8 A\$

I think this is the correct way to do it?