Question

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?

Answer 1

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