GATE EE 2013 Question Paper (10-Feb-2013) (Shift 2)

The impulse response of a continuous-time system is given by h(t) = δ(t-1) + δ(t-3)

The value of the step response at t = 2 is:

Two magnetically uncoupled inductive coils have Q factors q₁ and q₂ at the chosen operating frequency. Their respective resistances are R₁ and R₂. When connected in series, their effective Q factor at the same operating frequency is

The following arrangement consists of an ideal transformer and an attenuator which is attenuated by a factor of 0.8. An a.c.voltage ${\mathrm{V}}_{\mathrm{w}{\mathrm{x}}_1}=100V$ is applied across $\mathrm{WX}$ to get on the open-circuit voltage ${\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_1}$ across YZ. Next, an ac voltage ${\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_2}=100V$ is applied across YZ to get an open circuit voltage ${\mathrm{V}}_{\mathrm{W}{\mathrm{X}}_2}$ across $\mathrm{WX}$ , then

${\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_1}/{\mathrm{V}}_{\mathrm{W}{\mathrm{X}}_1},{\mathrm{V}}_{\mathrm{W}{\mathrm{X}}_2}/{\mathrm{V}}_{\mathrm{Y}{\mathrm{Z}}_2}$ are

Thyristor T is initially off and is triggered with a single pulse of width 10 μs. It is given that $L=\frac{100}{\pi }\mu H$ and $C=\frac{100}{\pi }\mu H.$ Assuming latching and holding currents of thyristors are both 0 and the initial charge of C is 0, T conducts for.

A 4 pole Induction motor, is supplied by a slightly unbalanced three-phase 50Hz source is rotating at 1440rpm. The electrical frequency in Hz of the induced negative sequence current in the rotor is