Solution to Question 4

To solve this, we will calculate the stress at the point where the strain gauge is mounted.

Given Data:

1. Gauge Factor (GF) = 2.4
2. Unstrained Resistance (R₀) = 120.0 Ω
3. Strained Resistance (R) = 120.1 Ω
4. Modulus of Elasticity (E) = $2 \times 10^6 \, \text{kg/cm}^2$

Step 1: Strain Calculation

The relationship between the gauge factor (GF), strain ($\varepsilon$), and resistance change is given by:

$\text{GF} = \frac{\Delta R / R_0}{\varepsilon}$

Where: $\Delta R = R - R_0 = 120.1 - 120.0 = 0.1 \, \Omega$

Substituting the values into the formula:

$\varepsilon = \frac{\Delta R}{R_0 \cdot\text{GF}}$

Substitute the values: $\varepsilon = \frac{0.1}{120.0 \cdot 2.4}$

$\varepsilon = \frac{0.1}{288.0} = 0.0003472 \, (\text{strain unit, no dimensions})$

Step 2: Stress Calculation

The stress ($\sigma$) is related to strain ($\varepsilon$) through the modulus of elasticity ($E$):

$\sigma = \varepsilon \cdot E$

Substitute the values: $E = 2 \times 10^6 \, \text{kg/cm}^2, \quad \varepsilon = 0.0003472$

$\sigma = 0.0003472 \cdot 2 \times 10^6$

$\sigma = 694.4 \, \text{kg/cm}^2$

Final Answer:

The stress at the point where the strain gauge is mounted is:

$\sigma = 694.4 \, \text{kg/cm}^2$

Solution to Question 5

Three Types of Displacement Transducers:

1. Linear Variable Differential Transformer (LVDT)

   • Advantages:
     • High accuracy and sensitivity.
     • Frictionless operation, leading to long lifespan.
     • Can measure both small and large displacements.
   • Disadvantages:
     • Requires AC power supply.
     • Sensitive to temperature variations.

2. Potentiometric Displacement Transducer

   • Advantages:
     • Simple and cost-effective.
     • Provides direct and linear output.
   • Disadvantages:
     • Limited lifespan due to wear and tear.
     • Lower accuracy compared to LVDTs.

3. Capacitive Displacement Transducer

   • Advantages:
     • High sensitivity and resolution.
     • Non-contact measurement possible.
   • Disadvantages:
     • Affected by environmental factors like dust and humidity.
     • Requires precise alignment during setup.

Let me know if you have further questions or want me to clarify!

Related Questions:

1. What other factors affect the stress calculation in strain gauges?
2. How is the modulus of elasticity different for various materials?
3. Can you explain more transducer types and their applications?
4. What is the importance of gauge factor in designing strain measurements?
5. How would environmental factors affect strain gauge readings?

Tip:

When using a strain gauge, always ensure proper calibration and environmental compensation to achieve accurate results.