Question

The primary coil of a linear variable differential transformer (LVDT) is supplied with AC voltage as shown in the figure. The secondary coils are connected in series opposition and the output is measured using a true RMS voltmeter. The displacement \(x\) of the core is indicated in mm on a linear scale. At the null position \(x = 0\), the voltmeter reads 0 V. If the voltmeter reads 0.2 V for a displacement of \(x = +2\) mm, then for a displacement of \(x = -3\) mm, the voltmeter reading, in V, is:

 

• A. \( -0.3 \)
• B. \( -0.1 \)
• C. \( 0.3 \)
• D. \( 0.5 \)

Hint:

The output voltage of an LVDT is directly proportional to the core displacement within its linear operating range. The sign of the output voltage indicates the direction of the displacement from the null position due to the series opposition of the secondary coils.

Answer 1

The Correct Option is A

Step 1: Understand the principle of LVDT.
An LVDT has a primary coil and two secondary coils connected in series opposition. When the core is at the null position (\(x=0\)), the induced voltages in the two secondary coils are equal in magnitude and opposite in phase, resulting in a net output voltage of 0 V.

Step 2: Recognize the linear relationship between output voltage and core displacement.
For small displacements around the null position, the output voltage of an LVDT is linearly proportional to the core displacement \(x\). The phase of the output voltage changes by 180 degrees as the core moves from one side of the null position to the other. This change in phase is often represented by a change in the sign of the output voltage.

Step 3: Determine the sensitivity of the LVDT.
We are given that for a displacement of \(x = +2\) mm, the voltmeter reads 0.2 V. The sensitivity (output voltage per unit displacement) of the LVDT can be calculated as:

\[ \text{Sensitivity} = \frac{\text{Output Voltage}}{\text{Displacement}} = \frac{0.2 \text{ V}}{+2 \text{ mm}} = 0.1 \text{ V/mm} \]
Step 4: Calculate the output voltage for a displacement of \(x = -3\) mm.
Using the sensitivity calculated in Step 3 and the given displacement of \(x = -3\) mm, the output voltage can be found as:

\[ \text{Output Voltage} = \text{Sensitivity} \times \text{Displacement} = 0.1 \text{ V/mm} \times (-3 \text{ mm}) = -0.3 \text{ V} \]
The negative sign indicates that the phase of the output voltage is opposite to that when the displacement was \(+2\) mm. The voltmeter reads the RMS value, and the sign indicates the phase relationship with the excitation voltage, which is reflected in the series opposition connection of the secondaries.