Engineering [Circuits] Calculating voltage and current in a circuit

[ainster31]

Homework Statement

Homework Equations

The Attempt at a Solution

How does the author do the below?

$$v_{ i }=2li=42V$$

What equation is he/she using?

 

[gneill]

That should be 21i. 21 Ω is the parallel combination of the 70 Ω and 30 Ω resistors. The author is calculating the voltage drop across that pair.

 

[ainster31]

That should be 21i. 21 Ω is the parallel combination of the 70 Ω and 30 Ω resistors. The author is calculating the voltage drop across that pair.

They seemed to have applied KCL at the middle node: $$i_1=i_2+I_0$$

But what about the other side of the same node? It looks like they only looked at the left-side of that node. Is that acceptable?

 

[gneill]

They seemed to have applied KCL at the middle node: $$i_1=i_2+I_0$$

But what about the other side of the same node? It looks like they only looked at the left-side of that node. Is that acceptable?

The current I_o takes care of whatever is happening on the other side; the node was partitioned in order to "get at" the current I_o . If you want, think of the horizontal wire as a zero ohm resistor separating two nodes