Summary of "Wheatstone Bridge: Working Principle & Formula"

Summary of “Wheatstone Bridge: Working Principle & Formula”

Main Ideas and Concepts

The Wheatstone Bridge is an electrical circuit designed to measure an unknown resistance by balancing two legs of a bridge circuit. The bridge consists of four arms labeled AB, BC, CD, and DA, each containing a resistor:

AB and BC: Known resistors, denoted as P and Q respectively (called ratio arms).
CD: Contains the unknown resistance, R.
DA: Contains a variable resistor, S.

A sensitive galvanometer (G) is connected between points B and D to detect current, while a battery is connected between points A and C to provide voltage.

Working Principle

The variable resistor S is adjusted until the galvanometer shows zero deflection, indicating no current flows through it.
At this balanced condition, the potential difference between points B and D is zero.
When balanced:
- The voltage drop across AB equals the voltage drop across AD.
- The voltage drop across BC equals the voltage drop across DC.
Using these equalities along with Ohm’s law, the relationship between the resistances is derived.

Key Equations

( i_1 \times P = i_2 \times R )
( i_1 \times Q = i_2 \times S )
Dividing equation (1) by (2) gives the formula for the unknown resistance ( R ):

[ R = \frac{P}{Q} \times S ]

Methodology / Steps to Determine Unknown Resistance

Connect the Wheatstone Bridge circuit with known resistors P and Q, variable resistor S, and unknown resistor R.
Connect the galvanometer across points B and D.
Connect the battery across points A and C.
Adjust the variable resistor S until the galvanometer reading is zero (bridge is balanced).
At balance, calculate the unknown resistance using the formula:

[ R = \frac{P}{Q} \times S ]