Question

How does a Wheatstone bridge measure unknown resistance?

Answer 1

A Wheatstone bridge is a classic circuit used to measure an unknown electrical resistance with high precision. Here’s how it works:

### **Wheatstone Bridge Basics**

The Wheatstone bridge consists of four resistors arranged in a diamond shape with a power source and a galvanometer (or another sensitive current measuring device) connected across the bridge. The four resistors are arranged as follows:

1. **R1 and R2** are known resistors (standard resistors).
2. **R3** is the known resistor, and **Rx** is the unknown resistor.
3. **R4** is the resistor that is adjusted to balance the bridge.

The bridge is powered by a voltage source, and the galvanometer is connected between the two midpoints of the bridge.

### **Measuring Unknown Resistance**

1. **Setup:** Connect the resistors as shown:
   - **R1** and **R2** are in one arm of the bridge.
   - **R3** and **Rx** (the unknown resistor) are in the other arm.
   - The galvanometer is connected between the junction of **R1** and **R3**, and the junction of **R2** and **Rx**.
   - A voltage source is connected across the bridge (one across R1 and R2, and the other across R3 and Rx).

2. **Balancing the Bridge:** Adjust **R4** (or a variable resistor in place of R4) until the galvanometer reads zero. This means that there is no current flowing through the galvanometer, and the bridge is balanced.

3. **Condition for Balance:** At balance, the ratio of the resistances in one arm of the bridge equals the ratio of the resistances in the other arm. Mathematically, this is expressed as:

   \[
   \frac{R1}{R2} = \frac{R3}{Rx}
   \]

4. **Calculating Unknown Resistance:** Rearrange the balance equation to solve for the unknown resistance \( Rx \):

   \[
   Rx = \frac{R3 \times R2}{R1}
   \]

   Here, \( R1 \), \( R2 \), and \( R3 \) are known resistors, and \( Rx \) is the unknown resistance you are measuring.

### **Why It Works**

The Wheatstone bridge works on the principle of null deflection. When the bridge is balanced, the ratio of the resistances ensures that the potential difference across the galvanometer is zero, meaning no current flows through it. This null condition allows for precise measurement because it eliminates the need for measuring current or voltage directly.

### **Applications**

The Wheatstone bridge is used not only for measuring unknown resistances but also for detecting small changes in resistance, such as in strain gauges, temperature sensors, and other precision measurements.

By adjusting the known resistors and achieving a balanced bridge, you can accurately determine the unknown resistance with minimal error.

Answer 2

A Wheatstone bridge is a fundamental electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. Here's a detailed explanation of how it works:

### Components of the Wheatstone Bridge

The Wheatstone bridge consists of four resistors arranged in a diamond shape:

1. **R1** and **R2**: These are known resistors connected in series to form one leg of the bridge.
2. **R3** and **Rx**: These are the other two resistors, where **Rx** is the unknown resistor and **R3** is a known resistor. They are connected in series to form the other leg of the bridge.
3. **A galvanometer**: This is an instrument used to detect the presence of current. It is connected between the two midpoints of the bridge legs.
4. **A voltage source**: This is connected across the two ends of the bridge.

### Bridge Configuration

Here’s how the components are arranged:

```
     R1
A -----/\/\/\/\----- B
|                   |
|                   |
|        G          |
|                   |
|                   |
C -----/\/\/\/\----- D
     R2             Rx
```

- **A** and **B** are the points where the voltage source is connected.
- **C** and **D** are the points where the galvanometer is connected.

### Working Principle

1. **Applying Voltage**: A voltage is applied across points A and B. This creates a potential difference across the bridge.

2. **Current Flow**: Current flows through the resistors R1 and R2, and also through R3 and Rx. This forms two separate loops in the bridge.

3. **Balance Condition**: The bridge is said to be "balanced" when the voltage across the galvanometer (between points C and D) is zero. When this happens, no current flows through the galvanometer. This implies that the potential difference between points C and D is equal, and thus the ratio of the resistances in one leg equals the ratio in the other leg. Mathematically, this is expressed as:

   \[
   \frac{R1}{R2} = \frac{R3}{Rx}
   \]

4. **Calculating Unknown Resistance**: Once the bridge is balanced (i.e., no current flows through the galvanometer), you can solve for the unknown resistance **Rx** using the balanced condition equation:

   \[
   Rx = R3 \times \frac{R2}{R1}
   \]

### Why It Works

The Wheatstone bridge relies on the principle of balance in electrical circuits. When the bridge is balanced, the voltage drop across the galvanometer is zero, indicating that the ratios of the known resistors are equal to the ratio of the unknown resistor. This precise measurement capability makes the Wheatstone bridge a valuable tool in both laboratories and practical applications for accurate resistance measurement.

In summary, the Wheatstone bridge measures an unknown resistance by creating a balance condition where the ratios of resistances in the two legs of the bridge are equal. This balance condition allows the unknown resistance to be calculated with high precision using the known values of the other resistors in the circuit.