Voltage at Vab, balancing, Increasing

[talaroue]

Homework Statement

R1=350 Ohms
R2=120 Ohms
R3=124 Ohms
R4=350 Ohms
A is between R1 and R4, while B is between R2 and R3. SORRY FOR NOT HAVING IT IN THE PICTURE
For the following circuit what is V_ab? Now balance the circuit so V_ab=0. After balancing what are the values of a shunt resistor which would increase V_ab by 2.75% ( a shunt resistor is a resistor which is placed in parallel to another resistor in order to change its value.)

Homework Equations

V_a=V_s R4(R1+R4)
V_b=V_s R3/(R2+R3)
Vab=Vb=Va

The Attempt at a Solution

So I basically have three parts to this problem. Find the value of V_ab, then balance it, then increase it.

for the the first part to find the value of V_ab

I just plug and chug for the above equations and got Va=2.5 V Vb=4.31 Vab=4.31-2.5=1.8 V that wasn't the hard part the hard part is that we didn't go over excatly how to do this but I found an example in the book but it just doesn't make since how to do the next two parts here is my work...if someone could do to things, tell me if I am right, and why! Because in physics its not really getting the right number it is why.

Balancing

R4=Rx
Rx=R1*R3/R2=(350*124)/120=362 Ohms

R2=Rx
Rx=R1*R3/R4=124 Ohms

R1=RX
RX=R2*R4/R3=339 Ohms

is that all I have to do? I realized that R3=Rx would be the same as R2 so i didn't think i had to change it but then I don't know what to do after that if there is another step.

THIRD PART increase V_ab by 2.75%

I have no idea it has work but it doesn't make sense where it comes from can someone explain to me how to do this part

I AM HORRIBLE WITH CIRCUITS! I AM CIVIL NOT ELECTRICAL

 

[talaroue]

any help would be awesome!

 

[tomcue]

Dear student,

It seems like you are on the right track with finding the value of Vab and balancing the circuit. However, I would like to clarify a few things to ensure that you have a complete understanding of the problem.

Firstly, in order to find Vab, you have correctly used the equations Va=Vs R4/(R1+R4) and Vb=Vs R3/(R2+R3). However, it seems like you have made a mistake in your calculation for Vb. It should be Vb=Vs R3/(R2+R3) = 2.5*(124/(120+124)) = 2.44 V. Therefore, Vab=Vb-Va = 2.44-2.5 = -0.06 V. This means that Vab is actually negative, indicating that the direction of current flow is from B to A.

Now, for balancing the circuit, the goal is to make the voltage at point A (Va) equal to the voltage at point B (Vb). This is achieved by making the resistance on either side of the circuit equal. In your attempt, you have correctly identified that R4 should be equal to Rx, and R2 should be equal to Rx. However, for R1, you have used the wrong equation. The correct equation for R1 should be R1=Rx*R3/R4=(362*124)/350=128.8 Ohms. Similarly, for R3, the correct equation is R3=Rx*R2/R1=(362*120)/128.8=337.8 Ohms. Therefore, the balanced circuit will have the following resistances: R1=128.8 Ohms, R2=362 Ohms, R3=337.8 Ohms, R4=362 Ohms.

For the third part, increasing Vab by 2.75%, you can use the equation Vab = Vb-Va = 2.5*(124/(120+124)) - 2.5*(128.8/(128.8+362)) = -0.06 V. In order to increase Vab by 2.75%, you would need to add a shunt resistor in parallel to R1. The equation for calculating the value of the shunt resistor is given by Vab = Vb-Va = 2.5*(124/(120+124))