- #1

NoahCygnus

- 96

- 1

- Homework Statement:
- Calculate the potential at point O in the section of the circuit shown in the diagram.

- Relevant Equations:
- ##\Sigma\Delta V = 0##

In this circuit, I have to find the potential at point O. I tried using Kirchhoff's voltage law for the three open loops AOC, AOB and BOC to arrive at potential at O. According to my calculations the potential at O should be 0, but that is not the case according to the source. So I must be using Kirchhoff's voltage rule wrong. So can anyone guide me how to work this problem using KVL?

Here's my calculation:

Using KVL on AOC:

##V_1 +I_1R_1 +V_O -I_3R_3 = V_3##

Manipulating this equation to arrive at:

##I_1R_1 +V_O -I_3R_3 = V_3 - V_1## (I)

KVL on AOB:

##V_1 +I_1R_1 +V_O - I_2R_2 = V_2##

Manipulation this to arrive at:

##I_1R_1 +V_O -I_2R_2 = V_2 - V_1## (II)

KVL on BOC:

##V_2 +I_2R_2 + V_O -I_3R_3 = V_3##

Manipulating this equation to arrive at:

##I_2R_2 + V_O-I_3R_3 = V_3 - V_2## (III)

Then using the three equations above to arrive at ##V_O##

## III-(I-II) ##

Do the math and we get ##V_O=0##

But the answer in the textbook is ##V_O=[V_1/R_1 +V_2/R_2 +V_3/R_3][1/R_1 +1/R_2 +1/R_3]^-1##.

What am I doing wrong?