A cylindrical 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 is $$1$$ pu. The critical clearing angle, in degrees, for a three-phase dead short circuit fault at the generator terminal is

The sequence components of the fault current are as follows:
$${{\rm I}_{positive}} = j1.5\,pu,\,\,{{\rm I}_{negative}} = - j0.5\,\,pu,$$
$${{\rm I}_{zero}} = - j1\,\,pu.$$ The typeof fault in the system is

The bus admittance matrix of a three-bus three-line system is
$$y = j\left[ {\matrix{ { - 13} & {10} & 5 \cr {10} & { - 18} & {10} \cr 5 & {10} & { - 13} \cr } } \right]$$
If each transmission line between the two buses is represented by an equivalent $$\pi \,$$ network, the magnitude of the shunt susceptance of the line connecting bus $$1$$ and $$2$$ is

L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals