GATE IN 2020 IN Q53: Sensors and Industrial Instrumentation

The mutual inductances between the primary coil and the secondary coils of a linear variable differential transformer (LVDT) shown in the figure are

and

. Assume that the self-inductances

and

remain constant and are independent of

. When

is in the range ±10 mm,

and

change linearly with

. At

mm or −10 mm, the change in the magnitudes of

and

is 0.25

. For a particular displacement

, the voltage across the detector becomes zero when

. The value of

(in mm, rounded off to one decimal place) is ____

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