GATE IN 2018 Question Paper (04-Feb-2018) (Shift 2)

The voltage and current drawn by a resistive load are measured with a 300 V voltmeter of accuracy ± 1% of full scale and a 5 A ammeter of accuracy ± 0.5% of full scale. The readings obtained are 200 V and 2.5 A. The limiting error (in %) in computing the load resistance is (up to two decimal places) ____.

A high Q coil having distributed (self) capacitance is tested with a Q-meter. First resonance at ω₁ = 10⁶rad/s is obtained with a capacitance of 990 pF. The second resonance at ω₂ = 2 ×10⁶rad/s is obtained with a 240 pF capacitance. The value of the inductance (in mH) of the coil is (up to one decimal place) ______.

The inductance of a coil is measured using the bridge shown in the figure. Balance (D = 0) is obtained with C₁ = 1 nF, R₁ = 2.2 MΩ, R₂ = 22.2 kΩ, R₄ = 10 kΩ. The value of the inductance Lₓ (in mH) is ______.

The average velocity v of flow of clear water in a 100 cm (inner) diameter tube is measured using the ultrasonic flow meter as shown in the figure. The angle θ is 45°. The measured transit times are t₁ = 0.9950 ms and t₂ = 1.0000 ms. The velocity v (in m/s) in the pipe is (up to one decimal place) ___.

A 1000 Ω strain gage (R${}_g$) has a gage factor of 2.5. It is connected in the bridge as shown in figure. The strain gage is subjected with a positive strain of 400 μm/m. The output Vₒ (in mV) of the bridge is (up to two decimal places) _____.