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

The circuit shown is driven by a sinusoidal input voltage, Vin resulting in the output voltage, Vout. The frequency (in kilohertz) at which the voltage gain is 0 dB is ________ (round off to two decimal places)

A conducting semi-circular loop of radius 𝑅 = 0.1 m, with its diameter centered at the origin, rotates in the x-y plane about the origin with a constant angular velocity, 𝜔 = 20 rad/s, as shown. A magnetic field of magnitude 𝐵 = 2 T and normal to x-y plane exists in the region 𝑥 ≥ 0 as shown. If the loop has a resistance of 2 Ω, and negligible inductance, the peak-to-peak current (in milliamperes) in the loop is __________ (round off to one decimal place)

In the circuit shown, R1 = 100 kΩ and R2 = 1 kΩ. If the base-to-emitter voltage of the npn BJT is 0.7 V and the collector-to-emitter voltage is 5.2 V, the 𝛽 (current gain) of the BJT is ________ (round off to two decimal places)

A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air = 8.854 × 10⁻¹² F/m). The radii of the inner and outer spheres are 𝑎 = 10 cm and 𝑏 = 15 cm, respectively. The capacitance (in picofarads) is ________ (round off to 2 decimal places)

A 1 kHz sine-wave generator having an internal resistance of 50 Ω generates an open-circuit voltage of 10 Vₚ₋ₚ. When a capacitor is connected across the output terminals, the voltage drops to 8 Vₚ₋ₚ. The capacitance of the capacitor (in microfarads) is _______ (round off to two decimal places)