An ideal transformer has 75 turns in the primary coil and n turns in the secondary coil. a 120 v rms 60hz ac voltage source is connected to the primary coil. a 10 ω resistor is connected to the secondary coil, forming a secondary circuit. the average power dissipated in the secondary circuit is 160 w. what is the number ns of turns in the secondary coil?

think you messed up the symbol for resistor as resistors are measured in ohms where the symbol used for ohms is Greek omega

solving for average power in secondary coil:

average power = (current rms) ^2*resistance⇒with a little algebra:

current rms = (√average power/resistance)

current rms=√160W/10Ω

current rms=4amps.

average power is also equal to current rms*voltage rms

with some algebra we can solve for voltage in the secondary wire:

voltage rms = average power / current rms

voltage rms = 160W/4A

voltage rms=40Volts

now that we have voltage in the soecondary we can solve for the amount of turns in the secondary: Voltage secondary/voltage primary=number of turns in secondary / number of turns in primary. using some algerbra we can solve for number of turns in secondary: (Voltage secondary/voltage primary) * number of turns in primary=number of turns in secondary

(40V/120V) * 75turns=number of turns in secondary

number of turns in secondary=25turns