Determine voltage in parallell circuit

[Teszla]

Determine voltage in circuit

Determine the voltage \[V_{1}\].
**broken link removed**

Is it possible to solve this with node voltage analysis?

 

[rahdirs]

Yes,it is possible.
Did you ask for an opinion/ a way to answer that ???

This looks like Hw,show what you've done to find V1

 

[Teszla]

I solved it by making a equivalent resistance for R and 4R, and then using voltage division. However I wonder if it's possible to also solve it with node voltage analysis. If it is, then, how?

 

[rahdirs]

Assume voltages at all the nodes.Say,GND at the negative end of battery,so positive of battery is at V0,the other end of 3R resistor is x,then the other end of R resistor is V1 + x.(See figure,if confused)
Write equations at node with voltage x,

x/3R - (V1+x - x)/R -(V1+x -x)/4R = 0
=> x = 15V1/4

Write equations at node with voltage V1 + x,

V1/4R + V1/R + (V1 + x - V0)/2R = 0
=>V1 = (4/29)V0

 

[Teszla]

Very useful answer. Thanks

 

[afridii]

your method is absolutely right, but i think for beginner the nodal method is assign(suppose with a variable) to each node and then apply KCL at each node, you will get as many equations as nodal voltage variables, onward is straight forward linear algebra and you will get your answer and a lot more details of that circuit will be at your finger tip as well.

you shown V1+x at a node, in my opinion just V1 is enough

regards!