GATE IN 2014 Question Paper (02-Feb-2014) (Shift 2)

The resistance of a wire is given by the expression

$R=\frac{4\rho L}{\pi D^2}$

where, ρ is the resistivity (Ω-meter),L is the length (meter) and D (meter) is the diameter of the wire. The error in measurement of each of the parameters ρ, L, and D is ±1.0% . Assuming that the errors are independent random variables, the percent error in measurement of R is _______.

The circuit shown in the figure contains a dependent current source between A and B terminals. The Thevenin’s equivalent resistance in kΩ between the terminals C and D is _________.

A thermistor has a resistance of 1 kΩ at temperature 298 K and 465 Ω at temperature 316 K. The temperature sensitivity in K⁻¹[i.e. (1/R)(dR/dT), where R is the resistance at the temperature T(in K)], of this thermistor at 316 K is ___________.

A barium titanate piezoelectric crystal with d₃₃ = 150 pC/N, C${}_{crystal}$ = 25pF and R${}_{crystal}$ = 10¹⁰ Ω is used to measure the amplitude of a step force. The voltage output is measured using a digital voltmeter with input impedance 10¹³ Ω connected acorss the crystal. All other capacitances may be neglected. A step force of 2 N is applied from direction “3” on the crystal. The time in milliseconds within which the voltmeter should sample the crystal output voltage so that the drop form the peak value is no more than 0.12 V is_________

A thermopile is constructed using 10 junctions of Chormel – Constantan (sensitivity 60 μv/°C for each junction) connected in series. The output is fed to an amplifier having an infinite input impedance and a gain of 10. The output from the amplifier is acquired using a 10-bit ADC, with reference voltage of 5 V. The resolution of this system in units of ° C is _________.