LVDT Sensitivity Calculation Explained

An LVDT (Linear Variable Differential Transformer) is a widely used sensor for measuring linear displacement. This problem requires us to calculate the sensitivity of an LVDT system, which includes an amplifier and a voltmeter.

Understanding the Given Information

To find the sensitivity, we first need to identify all the provided parameters:

• The input is a displacement of 0.5 mm.
• The LVDT produces a raw output voltage of 2 mV for this displacement.
• This raw output is passed through an amplifier with a gain of 250.
• The amplified signal is then fed to a voltmeter with a range of 0-5 V.

The sensitivity of an instrument is generally defined as the ratio of the change in output signal to the change in the input quantity it is measuring.

Calculating the Amplified Output Voltage

The first step is to determine the final output voltage that the voltmeter will display after the signal has been amplified. The LVDT's raw output needs to be converted from millivolts (mV) to Volts (V) for calculations.

Raw LVDT Output = $2 \text{ mV}$

Converting millivolts to Volts:

Raw LVDT Output = $2 \times 10^{-3} \text{ V}$

Now, we apply the amplifier's gain to this raw output:

Amplified Output Voltage = Raw LVDT Output $\times$ Amplifier Gain

Amplified Output Voltage = $(2 \times 10^{-3} \text{ V}) \times 250$

Amplified Output Voltage = $0.5 \text{ V}$

So, the voltmeter will read 0.5 V for a displacement of 0.5 mm.

Determining the Instrument Sensitivity

With the amplified output voltage calculated, we can now determine the overall sensitivity of the instrument system.

Sensitivity = $\frac{\text{Amplified Output Voltage}}{\text{Displacement}}$

Plugging in the values we have:

Sensitivity = $\frac{0.5 \text{ V}}{0.5 \text{ mm}}$

Sensitivity = $1 \text{ V/mm}$

Final Result Analysis

The calculated sensitivity for the instrument is 1 V/mm. This means that for every millimeter of displacement measured by the LVDT, the amplified output voltage increases by 1 Volt. This value matches one of the provided options.

The options given were:

• 0.1 V/mm
• 0.5 V/mm
• 1 V/mm
• 5 V/mm

Our calculated sensitivity of 1 V/mm corresponds to the third option.