Q$3.$ Ideal Transformer $(20$ points$)$

Consider an ideal transformer without any losses. As shown in the following circuit, the turn number ratio of the primary coil to the secondary coil is equal to $N_1$:$N_2=5.$ Given the $RMS$ value of the input voltage source $E$ is $240$ V $.$ We already know that the resistance of $R_1$ is $5,$ the resistance of $R_2$ is $0\mathrm{.}2,$ and the resistance of $R_3$ is $5.$ Now find:

$($a$)$ The RMS values of the primary current $(I_{pm})$ and the secondary current $(I_{sm}).$

$($b$)$ The active output power of the voltage source.