GATE Electrical Engineering (EE) 2018 Solved Paper

The positive, negative and zero sequence impedances of a three-phase generator are ${\mathit{z}}_1,{\mathit{z}}_2$ and ${\mathit{z}}_0$ respectively. For a line-to-line fault with fault impedance ${\mathit{z}}_{\mathit{r}\mathit{r}}$ the fault current is ${\mathit{I}}_{\mathit{f}1}=\mathit{k}{\mathit{I}}_{\mathit{f}\mathit{r}}$, where ${\mathit{I}}_{\mathit{f}}$ is the fault current with zero fault impedance. The relation between ${\mathit{Z}}_{\mathit{f}}$ and $\mathit{k}$ is