Nodal Analysis Help, 1 equation 2 unknowns

[eatsleep]

1.

2. V=IR, Nodal analysis



3. Based on where I have drawn my ground, V2=-10V, V1=3I. From this I should just have 1 equation with 1 unknown (if I have done this correct). My KCL equation for node V1 is (V3+10)/8 + (V3-3I)/2 + V3/12. I am stuck, I need to find an equation for I in terms of V3.

 

[gneill]

If you assume the potential at v3 is, well, v3, then what's the current through the 12Ω resistor?

 

[eatsleep]

If you assume the potential at v3 is, well, v3, then what's the current through the 12Ω resistor?

Oh wow, I=V3/12

 

[gneill]

Oh wow, I=V3/12

Watch the sign...

 

[rezeew]

I understand your struggle with nodal analysis and solving for unknowns. It can be a complex process, but with a solid understanding of the underlying principles and equations, it is possible to solve for the unknowns.

Firstly, let's review the equation V=IR, which is known as Ohm's law. This equation relates the voltage (V) across a resistor to the current (I) flowing through it, with the constant of proportionality being the resistance (R). This equation is fundamental in understanding the relationship between voltage and current in a circuit.

Moving on to nodal analysis, it is a method used to analyze the behavior of electrical circuits by applying Kirchhoff's current law (KCL) at each node. KCL states that the sum of currents flowing into a node must equal the sum of currents flowing out of that node. This allows us to write equations for each node and solve for the unknown variables, in this case, V3 and I.

In your KCL equation for node V1, you have correctly considered the currents flowing into and out of the node. However, to solve for I in terms of V3, we need to make use of the equation V=IR. Rearranging this equation, we get I=V/R. Now, we can substitute this into your KCL equation and solve for V3.

(V3+10)/8 + (V3-3(V3/12))/2 + V3/12 = 0

Simplifying this equation, we get:

V3/8 + V3/4 - V3/8 + V3/12 = 0

Combining like terms, we get:

V3/3 = 0

Therefore, V3=0. This means that I=0 as well, since there is no voltage drop across a resistor with no current flowing through it.

In conclusion, by using the equation V=IR and applying KCL at the node V1, we were able to solve for the unknown variable V3 and determine that I=0. Keep practicing and applying these principles, and you will become more confident in solving nodal analysis problems in the future.