Transformer example problem

Problem:

An ideal transformer with a 300 turn primary connected to a 480 V, 60 Hz supply line is to output 120 V from the secondary. If a 100 Ω resistor is connected across the secondary, determine: A) How many turns the secondary must have. B) The current through the resistor, C)The current drawn through the primary.

Solution:

Part A:

${\frac {V_{1}}{V_{2}}}={\frac {N_{1}}{N_{2}}}$

Where $V_{1}=$Voltage across primary, $V_{2}=$Voltage across secondary, $N_{1}=$ Number of turns in primary, $N_{2}=$ Number of turns in secondary

${\frac {480\ volts}{120\ volts}}={\frac {300}{N_{2}}}$

$N_{2}={\frac {300\cdot 120}{480}}\Rightarrow N_{2}=75\ turns$

Part B:

The voltage across the secondary is given in the problem statement as 120 volts. Using ohms law, $V=i\cdot R$, we can solve for the current.
$i_{2}={\frac {V_{2}}{R_{L}}}$

$i_{2}={\frac {120\ volts}{100\ ohms}}$