Question

An $LVDT$ has an output of $10mV$ across its terminals when the core moves through a distance of $4mm.$ The output of this LVDT is connected to a $10V$ voltmeter through an amplifier of gain $1000.$ If the milli-voltmerer scale has $100$ divisions and scale can read upto $1/5$ of a divsion. Then the resolution of the overall setup is ____ $\mu m$.

• A. 8

Answer 1

The correct option is A 8

$\text{Sensitivity of LVDT}\left(k_1\right)$

$=\frac{\text{Output voltage}}{\text{Displacement}}=\frac{10mV}{4mm}=2.5mV/mm$

$\text{Sensitivity of amplifier}\left(k_2\right)=1000$

$\text{Sensitivity of whole setup}=k_1\times k_2$

$=2.5mV/mm\times 1000=2.5V/mm$

$\text{Minimum voltage that can be read by voltmeter}$

$=10V\times \frac{1}{100}\times \frac{1}{5}=20mV$

$\text{Resolution of overall instrument}$

$=\frac{20mV}{2.5V/mm}=8\mu m$