GATE IN 2011 Question Paper (13-Feb-2011) (Shift-2)

For a copper-constantan (Type T) thermocouple, the junction potential $E$ (in $\mu V$) at $0{}^{\circ }C$ is given by $E=38.74\theta +3.3\times 10^{-2}{\theta }^2+2.07\times 10^{-4}{\theta }^3-2.2\times 10^{-6}{\theta }^4$ + higher order terms , assuming the cold junction compensation. The sensitivity of thermocouple at $100{}^{\circ }C$ is approximately

The temperature of a furnace is monitored at a distance of $50\text{ m}$ away. The temperature transmitter has a range of $0-500{}^{\circ }C$ and provides $4-20\text{ mA}$ current output. The measured temperature and the output current have a straight line relationship with positive slope. The temperature is determined from the voltage measured across a resistance of $500\Omega$ in the current loop. If the voltage measured across the resistance is $4\text{ V}$, the temperature of the furnace is

The core/cladding index difference of a single-mode optical fiber cable is $0.01$. The refractive index of the material of the core is $1.5$. The maximum angle of acceptance of the fiber is approximately equal to

The conventional way of expressing vibration is in terms of

The primary and secondary of an LVDT (stroke length $\pm 50\text{mm}$) are connected to a $3\text{ kHz}$ sinusoidal source and ideal semiconductor diode bridge-based phase sensitive demodulator circuit. The core of the LVDT remains static at $15\text{ mm}$ above the ideal null position. The frequency of the voltage observed at the input of the low-pass filter is