GATE IN 2022 Question Paper (06-Feb-2022) (Shift 2)

Monochromatic light of wavelength 532 nm is used to measure the absorption coefficient of a material in a UV-Visible Spectrophotometer. The measured light intensity after transmission through a 1 cm thick sample of the material is 0.414 mW/cm². For a sample of thickness 2 cm, the measured light intensity is 0.186 mW/cm². The absorption coefficient (in cm⁻¹) of the material is ________ (round off to two decimal places)

In the circuit shown, the load is driven by a sinusoidal ac voltage source V₁ = 100 ∠0° V at 50 Hz. Given R₁ = 20 Ω, ${\mathrm{C}}_1=\left(\frac{1000}{\pi }\right)\mu \mathrm{F},{\mathrm{L}}_1=\left(\frac{20}{\pi }\right)\mathrm{mH}$ and R₂ = 4 Ω, the power factor is ________ (round off to one decimal place)

In a unity-gain feedback control system, the plant

$\mathrm{P}(\mathrm{s})=\frac{0.001}{\mathrm{s}(2s+1)(0.01s+1)}$

is controlled by a lag compensator

$\mathrm{C}(\mathrm{s})=\frac{\mathrm{s}+10}{\mathrm{s}+0.1}$

The slope (in dB/decade) of the asymptotic Bode magnitude plot of the loop gain at 𝜔 = 3 rad/s is ________ (in integer)

Given Circuit A with currents I₁ and I₂ as shown, the current I₃ in Circuit B (in amperes), is ________(round off to one decimal place)

In the balanced three-phase circuit shown, C₀ = 8.2 μF and the line-to-line r.m.s. voltage is 440 V at 50 Hz. The reading on the wattmeter (in watts) is _______ (round off to two decimal places)