GATE EE 2016 Question Paper (06-Feb-2016) (Shift 2)

A single-phase transmission line has two conductors each of $10mm$ radius. These are fixed at a center-to-center distance of $1m$ in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance $D$ from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three-phase system is to be $5\%$ more than that of the inductance per conductor of the single-phase system. The distance $D$, in meters, is _______.

In the circuit shown below, the supply voltage is 10 sin (1000 t) volts. The peak value of the steady-state current through the 1Ω resistor, in amperes, is ______.

A dc voltage with ripple is given by V(t) = [100 + 10 sin (ωt) - 5 sin (3ωt)] volts. Measurements of this voltage v(t), made by moving-coil and moving-iron voltmeters, show, readings of V₁ and V₂ respectively. The value of V₂ - V₁, in volts, is _________.

The circuit below is excited by a sinusoidal source. The value of R, in Ω, for which the admittance of the circuit becomes a pure conductance at all frequencies is _____________.

In the circuit shown below, the node voltage V${}_A$ is ___________ V.