A physics lab is designed to study the transfer of electrial energy from one circuit to another by means of a magnetic field using simple transformers. Each transformer has two coils of wire electrically insulated from each other but wound a round a common core of ferromagnetic material. The two wires are close together but do not touch each other The primary `(1^(@))` coil is connected to a source of alternating `(AC)` current. The secondary `(2^(@))` coil is connected to resistor such as a light bulb. The `AC` source produces on oscillating voltage and current in the primary coil that produces an oscillating megnetic field in the core. material. This in turn induces an oscillating voltage and `AC` curent in the secondary coil Students collected the following data comparing the number of turns per coil `(N)`, the voltage `(V)` and the current `(I)` in the coils of three transformers. `|{:("Transformer","primary coil","Secondary coil"),(1,100 . 10V.10A,200.20V.5A),(2,100.10V.10A,50.5V.5A),(3,100.10V.10A,100.5V.20A):}|` Which of the following is a correct expression for `R`, the resistance of the load connected to the secondary coilA. `((V_(1^(@)))/(I_(1^(@))))((N_(2^(@)))/(N_(1^(@))))`B. `((V_(1^(@)))/(I_(1^(@))))((N_(2^(@)))/(N_(1^(@))))^(2)`C. `((V_(1^(@)))/(I_(1^(@))))((N_(1^(@)))/(N_(2^(@))))`D. `((V_(1^(@)))/(I_(1^(@))))((N_(1^(@)))/(N_(2^(@))))^(2)`