Wheatstone Bridge

The Wheatstone bridge is a fundamental electrical circuit used for the precise measurement of electrical resistances. It was invented by Samuel Hunter Christie in 1833 and popularized by Sir Charles Wheatstone in 1843. The bridge is especially useful for measuring unknown resistances and for calibrating measuring instruments.

Principle of Operation

The Wheatstone bridge operates on the principle of null deflection, i.e., the condition of no current flow through the galvanometer connected in the bridge. The bridge consists of four resistances, a galvanometer, and a voltage source. When the bridge is balanced, the ratio of the two resistances in one arm is equal to the ratio of the two resistances in the other arm, and no current flows through the galvanometer.

Circuit Diagram

A typical Wheatstone bridge circuit is illustrated below:

      (R1)       (R2)
  A ----\/\/\/----\/\/\/---- B
     |                     |
    (V)                   (G)
     |                     |
  D ----\/\/\/----\/\/\/---- C
      (Rx)       (R3)

Where:

• R1, R2, and R3 are known resistances
• Rx is the unknown resistance
• V is the voltage source
• G is the galvanometer

Formulas

The condition for the bridge to be balanced (no current through the galvanometer) is given by the equation:

$$ \frac{R1}{R2} = \frac{Rx}{R3} $$

From this equation, we can solve for the unknown resistance Rx:

$$ Rx = R3 \cdot \frac{R1}{R2} $$

Balancing the Bridge

To balance the bridge, you can adjust the known resistances until the galvanometer shows zero deflection. At this point, the above equation holds true, and you can calculate the unknown resistance.

Differences and Important Points

Here is a table summarizing the key aspects of the Wheatstone bridge:

Feature	Description
Purpose	Used to measure unknown resistances with high precision.
Principle	Based on the null deflection method.
Components	Four resistances, a galvanometer, and a voltage source.
Balanced Condition	No current flows through the galvanometer when the bridge is balanced.
Equation	( \frac{R1}{R2} = \frac{Rx}{R3} )

Examples

Example 1: Calculating Unknown Resistance

Suppose you have a Wheatstone bridge with the following known resistances: R1 = 100Ω, R2 = 200Ω, and R3 = 150Ω. The bridge is balanced. Calculate the unknown resistance Rx.

Using the formula:

$$ Rx = R3 \cdot \frac{R1}{R2} $$

$$ Rx = 150Ω \cdot \frac{100Ω}{200Ω} $$

$$ Rx = 150Ω \cdot 0.5 $$

$$ Rx = 75Ω $$

The unknown resistance Rx is 75Ω.

Example 2: Adjusting the Bridge

If R1 = 50Ω, Rx = 100Ω, and R3 = 100Ω, find the value of R2 that balances the bridge.

Using the formula:

$$ \frac{R1}{R2} = \frac{Rx}{R3} $$

$$ \frac{50Ω}{R2} = \frac{100Ω}{100Ω} $$

$$ R2 = 50Ω $$

The value of R2 that balances the bridge is 50Ω.

Conclusion

The Wheatstone bridge is a powerful tool in electrical measurements. By understanding its principles and operation, one can accurately determine unknown resistances and ensure the precision of electrical instruments. It is essential for students and professionals in the field of electronics and electrical engineering to be familiar with the Wheatstone bridge for both theoretical and practical applications.