Get Expert Help with Wheatstone Bridge Circuit Analysis - 15mV Voltage Given

In summary, you need to write a KCL equation for the bottom two resistors in order to find their voltage.
  • #1
James889
192
1
Hi,

I have this circuit:
[PLAIN]http://img813.imageshack.us/img813/1189/wheatstone.png [Broken]

All resistors are 1K except Rx which is unknown.
The voltage across the terminals are given to be 15mV.

Im assuming i have to write a KCL equation but I am not sure how.

Any hints?
 
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  • #2
Write KCL for the loop containing R1 and R2 and find the voltage at the node between the two resistors. Do the same thing for the loop containing R3 and Rx (it will be a funtion of Rx).
The voltage difference between the two nodes is 15 mV.
 
  • #3
So i have
[tex]2000i_1 = 18[/tex]

Which gives i1 = 9mA

And thus

[tex]24mA(1000+R_x) = 18[/tex]

But 18/24mA = 750

Subtracting 1000 gives Rx = -250:confused:
 
  • #4
I don't see where the 24? came from.

The second KCL loop would be:
18 = i2(1000 + Rx)
If you write a loop for the bottom two resistors you can say:
15 mV = 9 mA (1000) - i2(Rx)
Then 8.85 = i2(Rx) → Rx = 8.85/ i2
Substituting back into the previous equation gets you:
18 = i2(1000 + 8.85/ i2)
18 = 1000 i2 + 8.85
i2 = 9.15 mA and Rx = 967
 
  • #5
In this case, you can work the answer out with Ohm's Law.

You know the voltage at the left centre point has to be half the supply voltage (because R1 and R2 are equal) and the voltage at the right centre point has to be 0.015 volts less than this (relative to the negative supply terminal).

So, you can work out the current in the top right 1K resistor and hence work out the size of the bottom right resistor, which must have the same current and you know the voltage across it.
 
Last edited:
  • #6
woomerp said:
I don't see where the 24? came from.

The second KCL loop would be:
18 = i2(1000 + Rx)
If you write a loop for the bottom two resistors you can say:
15 mV = 9 mA (1000) - i2(Rx)


Hm, so you can write a loop equation for the bottom two resistors even though they really aren't forming a loop?
 

What is a Wheatstone bridge?

A Wheatstone bridge is a circuit used to measure unknown electrical resistances. It consists of four resistors connected in a diamond shape, with an input voltage source and a galvanometer connected to the two opposite points.

How does a Wheatstone bridge work?

A Wheatstone bridge works by balancing the ratio of resistances on each side of the circuit. When the resistances are balanced, no current flows through the galvanometer, indicating that the resistance being measured is equal to the known resistances in the bridge.

What is the purpose of a Wheatstone bridge?

The primary purpose of a Wheatstone bridge is to accurately measure unknown resistances. It is often used in scientific and engineering experiments to measure the resistance of materials or components.

What are the components of a Wheatstone bridge?

The components of a Wheatstone bridge include four resistors, an input voltage source, and a galvanometer. The resistors are typically labeled R1, R2, R3, and R4, and the galvanometer is often labeled G.

What are some common applications of a Wheatstone bridge?

Wheatstone bridges have many practical applications, including measuring the resistance of materials, testing the accuracy of sensors, and calibrating electrical equipment. They are also commonly used in strain gauge measurements, where changes in resistance can indicate changes in strain or pressure.

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