Deriving the Wheatstone Bridge Equation with Respect to R3 - Math Nerd Help

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In summary, the Wheatstone Bridge equation is a mathematical formula used to calculate the value of an unknown resistor in a bridge circuit. It is derived using a combination of Ohm's law and Kirchhoff's laws, and the role of R3 in the equation is to represent the unknown resistor. This equation has many real-world applications, such as in electronic circuits and measurements, but it has limitations as it assumes ideal resistors and only works for balanced circuits.
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mhrobson
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I need to derive the following equation with respect to R3. This is the equation for a Wheatstone bridge. Unfortunately I am not very good at derivations. Here is the equation:
VO=((R3/(R2+R3))-(R4/(R1+R4)))VS

I came up with the following answer but was told that it is wrong:
dVO/dR3 = ((1/(R2+R3))-(R3/(R2+R3)2)VS

If you want to be a real sport, set R1=R3 and derive the same expression.
 
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Suppose [tex]y=((x/(12+x))-(4/(12+4)))\cdot 6[/tex], can you do dy/dx now?
 

FAQ: Deriving the Wheatstone Bridge Equation with Respect to R3 - Math Nerd Help

What is the Wheatstone Bridge equation?

The Wheatstone Bridge equation is a mathematical formula used to calculate the value of an unknown resistor in a bridge circuit. It is based on the principle of balancing two parallel branches of resistors, and is commonly used in electronic circuits and measurements.

How is the Wheatstone Bridge equation derived?

The Wheatstone Bridge equation is derived using a combination of Ohm's law and Kirchhoff's laws. By applying these laws to a balanced bridge circuit, we can create a system of equations that can be solved to find the value of the unknown resistor.

What is the role of R3 in the Wheatstone Bridge equation?

R3 is the unknown resistor in the Wheatstone Bridge circuit. Its value is what we are trying to find using the Wheatstone Bridge equation. The other resistors in the circuit are known values, and R3's value can be calculated by solving the equation.

How can the Wheatstone Bridge equation be used in real-world applications?

The Wheatstone Bridge equation is often used in electronic circuits and measurements, such as in strain gauges, temperature sensors, and pressure sensors. It is also used in bridge circuits to accurately measure resistance and balance voltage levels.

Are there any limitations to the Wheatstone Bridge equation?

The Wheatstone Bridge equation assumes that the resistors in the circuit are ideal and have no internal resistance. In real-world applications, this may not always be the case and can lead to some inaccuracies in the calculated value of R3. Additionally, the equation is only applicable to balanced bridge circuits and may not work for unbalanced circuits.

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