GATE EE 2012 Question Paper (12-Feb-2012) (Shift 2)

Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)ⁿ u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = ½, then g[1] equals

The circuit shown is a

For the system below, S${}_{D1}$ and S${}_{D2}$ are complex power demands at bus 1 and bus 2 respectively. If |V₂| = 1 pu, the VAR rating of the capacitor ( Q${}_{G2}$) connected at bus 2 is

A cylinder rotor generator delivers 0.5 pu power in the steady – state to an infinite bus through a transmission line of reactance 0.5 pu. The generator no-load voltage is 1.5 pu and the infinite bus voltage is 1 pu. The inertia constant of the generator is 5 MW – s / MVA and the generator reactance in 1 pu. The critical clearing angle, in degrees, for a three – phase dead short circuit fault at the generator terminal is

In the circuit shown, an ideal switch S is operated at 100 KHz with a duty ratio of 50%. Given that Δ i${}_c$ is 1.6 A peak to peak and Iₒis 5 A dc, the peak current in S is