Wheatstone bridge is an arrangement of _____ resistors used for accurate measurement of resistance.
Understanding the Wheatstone Bridge Circuit
The Wheatstone bridge is a fundamental electrical circuit widely used for precisely measuring an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
This circuit arrangement is particularly useful because it allows for very sensitive measurements compared to simple methods like using an ohmmeter, especially when the bridge is balanced.
Key Components of a Wheatstone Bridge
A standard Wheatstone bridge circuit is constructed using several key components. At its heart, the arrangement consists of resistors forming the four arms of the bridge. These arms are connected to a galvanometer and a voltage source (like a battery or power supply).
Specifically, the classical setup of a Wheatstone bridge includes:
- Three resistors of known resistance. One or two might be fixed, and one is typically a variable resistor (often called a rheostat or decade box) used to balance the bridge.
- One resistor with an unknown resistance value that you want to measure.
- A galvanometer, which is a sensitive current-detecting instrument connected across two points of the bridge (the detector arm). It indicates if current is flowing through it.
- A voltage source (like a DC battery) connected across the other two points of the bridge, providing the potential difference.
Therefore, the core structure of the bridge itself, comprising the arms where resistances are placed, involves four resistors.
| Component | Description |
|---|---|
| Resistors | Typically four resistors forming the arms of the bridge (three known, one unknown). |
| Galvanometer | Detects current flow in the bridge's balance arm. |
| Voltage Source | Supplies power to the bridge circuit. |
How the Wheatstone Bridge Works
The principle of the Wheatstone bridge relies on achieving a balanced condition. The bridge is balanced when there is no current flowing through the galvanometer. This occurs when the potential difference across the galvanometer is zero.
In a balanced Wheatstone bridge with resistors $R_1, R_2, R_3,$ and $R_4$ in the four arms, the following relationship holds:
\begin{equation} \frac{R_1}{R_2} = \frac{R_3}{R_4} \end{equation}
If $R_1, R_2,$ and $R_3$ are known (with $R_3$ often being the variable resistor used for balancing) and $R_4$ is the unknown resistance, its value can be calculated once the bridge is balanced using the formula:
\begin{equation} R_4 = R_3 \times \frac{R_2}{R_1} \end{equation}
By adjusting the variable resistor ($R_3$) until the galvanometer shows zero deflection (indicating no current), the bridge becomes balanced. At this point, the known values of $R_1, R_2,$ and $R_3$ (specifically the value of the variable resistor at balance) are used to determine the unknown resistance $R_4$.
Applications of the Wheatstone Bridge
The Wheatstone bridge is used in various applications requiring precise resistance measurement, including:
- Measuring unknown resistances accurately.
- As the basis for various sensors that change resistance with physical changes (like strain gauges, temperature sensors, pressure sensors), where the sensor forms one arm of the bridge.
- In control systems.
The fundamental setup always involves the four resistor arms to create the potential differences that are compared for balancing.
Revision Table: Wheatstone Bridge Facts
| Feature | Description |
|---|---|
| Purpose | Accurate resistance measurement |
| Number of Resistor Arms | Four |
| Balancing Condition | No current through galvanometer |
| Key Principle | Ratio of resistances in arms is equal at balance |
Additional Information on Wheatstone Bridge Concepts
While the standard Wheatstone bridge uses four resistor arms, variations exist, but the basic measurement principle for resistance relies on this configuration. The sensitivity of the bridge depends on the values of the resistors and the sensitivity of the galvanometer. For very low or very high resistances, modified bridges like the Kelvin bridge are used.
The Wheatstone bridge demonstrates the concept of null detection, where the measurement is made when the indicator (galvanometer) shows zero, which often allows for higher accuracy as it doesn't rely on the linearity or calibration of the indicator instrument itself, only its ability to detect zero current.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
