GATE IN 2021 Question Paper (06-Feb-2021) (Shift 1)

A bar primary current transformer of rating 1000/1 A, 5VA, UPF has 995 secondary turns. It exhibits zero ratio error and phase error of 30 minutes at 1000 A with rated burden. The watt loss component of the primary excitation current in ampere is ________ (rounded off to one decimal place)

In the bridge circuit shown, the voltmeter V showed zero when the value of the resistors are: R1 = 100 Ω, R2 = 110 Ω, and R3 = 90 Ω. If (R1/R2) = (RA/RB), the value of R4 in ohm is _____.

For the full bridge made of linear strain gages with gage factor 2 as shown in the diagram, R₁ = R₂= R₃ = R₄ = 100 Ω at 0°C and strain is 0. The temperature coefficient of resistance of the strain gages used is 0.005 per °C. All strain gages are made of same material and exposed to same temperature. While measuring a strain of 0.01 at a temperature of 50°C, the output V${}_O$ in millivolt is _____ (rounded off to two decimal places).

A signal having a bandwidth of 5 MHz is transmitted using the Pulse code modulation (PCM) scheme as follows. The signal is sampled at a rate of 50% above the Nyquist rate and quantized into 256 levels. The binary pulse rate of the PCM signal in Mbits per second is ___.

In the figure shown, a large multimode fiber with n${}_{core}$ = 1. 5 and n${}_{clad}$ = 1. 2 is used for sensing. A portion with the cladding removed passes through a liquid with refractive index n${}_{liquid}$. An LED is used to illuminate the fiber from one end and a paper is placed on the other end, 1 cm from the end of the fiber. The paper shows a spot with radius 1 cm. The refractive index n${}_{liquid}$ of the liquid (rounded off to two decimal places) is ____________.