A step up transformer which has the following nameplate data. Voltage rating: $20/100300500$ kV Current rating: $1050/111$ A$.$ If a cable that has SF$6$ gas insulation $($Cb $=60$ pF$)$ with a length of $6$ km is tested on a transformer according to the rating above. The short circuit test results were obtained as follows, the voltage was $15$ kV$,$ the current was $1050$ A$,$ and the power was $3\mathrm{.}2$ kW$.$ After that, an open circuit test was carried out, and the value for voltage $1$ was $100$ V$,$ voltage $2$ was $500$ kV$,$ the measured current was $62$ A$,$ and the power obtained was $7\mathrm{.}3$ kW$.$ Design: a$.$ Replacement circuit for test transformers during open and short circuit conditions b$.$ If the test transformer above uses a secondary output rating of $500$ kV$,$ determine the secondary voltage value of the transformer if the primary voltage provided is $20$ kV