For the first assignment, consider the grid to be ideal, so $Z_{\text{g}\text{r}\text{i}\text{d}}=0.$ We use an electric furnace, which consists of three identical cooking plates with an impedance of $R+jL.$ For proper operation each cooking plate should be connected to a $231$ V supply.

a$.$ How can you connect the furnace to each of the three given power supplies $(1231V,3231V$ and $3400V)?$ Draw the circuit diagrams for each situation and indicate the line voltages and phase voltages, line currents and phase currents in these schemes.

Single phase $1$x$231$V@$50$Hz

L O

NO

Threephase $3$x$231$V@$50$Hz

L$1$O

L$2$O

L$3$O

Threephase $3$x$400$V@$50$Hz

L$1$O

L$2$O

L$3$O