Question

How do you calculate the equivalent resistance of resistors in a Wheatstone bridge?

Answer 1

To calculate the equivalent resistance of resistors in a Wheatstone bridge, you can follow these steps:

Identify the Wheatstone Bridge Configuration:
A Wheatstone bridge consists of four resistors arranged in a diamond shape. Two of the resistors are connected in series on one side, and the other two are connected in series on the opposite side. A voltage source is connected across one diagonal, and the other diagonal is connected to a galvanometer or some other measuring device.

The general configuration of a Wheatstone bridge is:

diff
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  R1         R3
-----  |-----|-----|
|    | |     |     |
| Vs | |     |     |
|    | |     |     |
-----  |-----|-----|
  R2         R4


Write Down the Balanced Bridge Equation:
For a Wheatstone bridge to be balanced (no current flows through the galvanometer), the ratio of resistances on one side must be equal to the ratio on the other side. Mathematically, this can be expressed as:

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R1 / R2 = R3 / R4


Calculate the Equivalent Resistance:
The equivalent resistance, often denoted as Req, is the value of a single resistor that would replace the entire Wheatstone bridge while maintaining the same current flow. This equivalent resistance can be calculated using the balanced bridge equation. Solve the equation for Req:

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Req = (R1 * R2) / (R1 + R2)


Alternatively, you can use the other ratio:

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Req = (R3 * R4) / (R3 + R4)


Substitute Values and Calculate:
Plug in the values of the individual resistors (R1, R2, R3, R4) into the appropriate formula and perform the calculations. Make sure all resistances are in the same units, typically ohms (Ω).

That's how you calculate the equivalent resistance of resistors in a Wheatstone bridge. This equivalent resistance is useful for understanding the overall behavior of the Wheatstone bridge circuit and for determining its sensitivity and accuracy in measuring unknown resistances.