GATE IN 2023 Question Paper (11-Feb-2023) (Shift-1)

A wire-wound ‘resistive potentiometer type' angle sensor with 72 turns is used in an application. The first turn of the potentiometer is connected to ground while its last turn is connected to 3.6 V. The width of the wiper covers two turns ensuring make-before-break. The output (wiper) voltage when the wiper is on top of both the turns 35 and 36 is ________ V (rounded off to two decimal places).

The two secondaries of a linear variable differential transformer (LVDT) showed a magnitude of 2 V (RMS) for zero displacement position of the core. It is noted that the phase of one of the secondaries has a deviation of one degree from the expected phase. Other than this deviation, the LVDT is ideal.
If the differential output sensitivity of the LVDT is 1 mV (RMS)/1 $\mu$ m, the output for zero displacement is ________ $\mu$ m (rounded off to one decimal place).

Five measurements are made using a weighing machine, and the readings are 80 kg, 79 kg, 81 kg, 79 kg and 81 kg. The sample standard deviation of the measurement is ________ kg (rounded off to two decimal places).

Four strain gauges $R_A,R_B,R_C$ and $R_D$, each with nominal resistance $R$, are connected in a bridge configuration. When a force is applied, $R_A$ and $R_D$ increase by $\Delta R$ and $R_B$ and $R_C$ decrease by $\Delta R$ as shown. A potentiometer with total resistance $R_v$ is connected as shown. If $R=100\Omega$, and $\Delta R=1\Omega$, the minimum value of resistance $R_v$ required to balance the bridge is ________ $\Omega$ (rounded off to two decimal places).

A sinusoidal current of $i_1(t)=1\sin (200\pi t)$ mA is flowing through a 4 H inductor which is mutually coupled to another 5 H inductor carrying

$i_2(t)=2\sin (200\pi t)$ mA

as shown in the figure. The coupling coefficient between the inductors is 0.6. The peak energy stored in the circuit is ________ $\mu$ J (rounded off to two decimal places).