# How do I calculate i, i1, i2 and v2? I'm unable to figure out how to use the current dependant voltage source in KVL

The following are the equations I've found, up till now: 20i+V2=10, V2=50i1, 20i+50i1=10, i=i1+i2

• Use mesh analysis. Update your question with the equations you found and we will help you along. Feb 8 '20 at 12:19
• updating your question means editing it, @Aimen: That way, others don't have to read all through the comments here. Feb 8 '20 at 12:22
• You're on the right way. There is another way to write out V2, i.e. using the components between nodes b and c and between c and d. (BTW, you need to use 2 spaces at the end of a line to start text on a new line) Feb 8 '20 at 12:32
• What happened to the 25 ohm resistor? It is not in your equations. (And no, in this circuit you can't ignore it) Feb 8 '20 at 12:37
• @Jan Yes I know, I got the right answers now. Thank you. Feb 8 '20 at 15:32

Well, we are trying to analyze the following circuit: simulate this circuit – Schematic created using CircuitLab

Using KCL, we can write:

$$\text{I}_1=\text{I}_2+\text{I}_3\tag1$$

Using KVL, we can write:

$$\begin{cases} \text{I}_1=\frac{\text{V}_\text{a}-\text{V}_1}{\text{R}_1}\\ \\ \text{I}_2=\frac{\text{V}_2}{\text{R}_2}\\ \\ \text{I}_3=\frac{\text{V}_1}{\text{R}_3}\\ \\ \text{V}_\text{x}=\text{V}_1-\text{V}_2=\alpha\text{I}_1 \end{cases}\tag2$$

Using some Mathematica code:

FullSimplify[
Solve[{I1 == I2 + I3, I1 == (Va - V1)/R1, I2 == V2/R2, I3 == V1/R3,
Vx == V1 - V2 == α*I1}, {I1, I2, I3, V1, V2, Vx}]]


FullSimplify[
Solve[{I1 == I2 + I3, I1 == (10 - V1)/20, I2 == V2/25, I3 == V1/50,
Vx == V1 - V2 == 5*I1}, {I1, I2, I3, V1, V2, Vx}]]


Which gives:

{{I1 -> 1/4, I2 -> 3/20, I3 -> 1/10, V1 -> 5, V2 -> 15/4, Vx -> 5/4}}


Which approximate to:

{{I1 -> 0.25, I2 -> 0.15, I3 -> 0.1, V1 -> 5., V2 -> 3.75,
Vx -> 1.25}}

• Alright, I got it. Thank you very much for the help 😊 Feb 8 '20 at 13:10
• @Aimen You're welcome, I'm glad that I could help.
– Jan
Feb 8 '20 at 13:11
• Please stop giving away homework solutions. Feb 8 '20 at 13:26