GATE EE 2021 Question Paper (07-Feb-2021) (Shift 1)

If the input x(t) and output y(t) of a system are related as y(t) = max (0, x(t)), then the system is

Consider a large parallel plate capacitor. The gap d between the two plates is filled entirely with a dielectric slab of relative permittivity 5. The plates are initially charged to a potential difference of V volts and then disconnected from the source. If the dielectric slab is pulled out completely, then the ratio of the new electric field E2 in the gap to the original electric field E1 is ___________.

In the given circuit, the value of capacitor C that makes current I = 0 is ____________ μF.

In the circuit shown, a 5 V Zener diode is used to regulate the voltage across load R₀. The input is an unregulated DC voltage with a minimum value of 6 V and a maximum value of 8 V. The value of R${}_S$ is 6 Ω. The Zener diode has a maximum rated power dissipation of 2.5 W. Assuming the Zener diode to be ideal, the minimum value of R₀ is _________ Ω.

A 1 μC point charge is held at the origin of a cartesian coordinate system. If a second point charge of 10 μC is moved from (0, 10, 0) to (5, 5, 5) and subsequently to (5, 0, 0), then the total work done is _________ mJ.

(Round off to 2 decimal places).

Take $\frac{1}{4\pi {\epsilon }_o}=9\times 10^9$ in SI units. All coordinates are in meters.