1. What a Wheatstone Bridge Is
The Wheatstone bridge is a simple circuit used to measure an unknown resistance by comparing it with known resistances. It works by adjusting the circuit until the bridge is perfectly balanced, meaning no current flows through the galvanometer. At that point, the ratio of resistances becomes exact.
It is widely used because it gives very accurate measurements when the balance point is found correctly.
2. Basic Structure of the Wheatstone Bridge
The Wheatstone bridge is made of four resistances arranged in a diamond shape. A galvanometer connects the two opposite points, and a voltage source is applied across the other two points.
The resistances are usually labelled as P, Q, R (known), and S (unknown).
2.1. The Four Arms of the Bridge
- P and Q are known resistances forming one pair.
- R is another known resistance.
- S is the unknown resistance.
A galvanometer is placed between the junctions of these two pairs.
3. Principle of the Wheatstone Bridge
The Wheatstone bridge works on the principle of balanced ratios of resistances. When the galvanometer shows zero deflection, the bridge is said to be in balance. At this point, the potential difference between the galvanometer terminals becomes zero.
3.1. Condition for Balance
When the bridge is balanced:
\( \dfrac{P}{Q} = \dfrac{R}{S} \)
This relation allows us to find the unknown resistance S.
3.1.1. Meaning of the Balance Condition
The ratio of resistances in one branch must match the ratio in the other branch. This ensures no current flows through the galvanometer.
4. Finding the Unknown Resistance
Once the bridge is balanced, the unknown resistance can be calculated directly using:
\( S = R \dfrac{Q}{P} \)
4.1. Small Example
If the balancing condition gives P = 10 Ω, Q = 20 Ω, and R = 5 Ω, then:
\( S = 5 \times \dfrac{20}{10} = 10\,\Omega \)
5. Why No Current Flows at Balance
When the ratios match, both galvanometer terminals reach the same potential. Since current flows only when there is a potential difference, the galvanometer shows zero deflection. This zero-current point gives the most accurate comparison of resistances.
5.1. Energy Interpretation
The galvanometer detects even tiny differences in voltage. At balance, the energy difference between its ends becomes zero, indicating perfect ratio matching.
6. Applications of Wheatstone Bridge
The Wheatstone bridge is used wherever accurate measurement of resistance is required. It is especially useful in laboratory setups and in instruments like strain gauges and sensor circuits.
6.1. Where It Is Commonly Used
- Measurement of unknown resistances
- Calibration of electrical instruments
- Sensor circuits (strain gauges, temperature sensors)
- Meter bridge setups
7. Simple Way to Visualise It
Imagine balancing a scale: one side has known weights and the other has an unknown object. You adjust the weights until the scale balances. The Wheatstone bridge does the same thing, but with resistances.