Question

Electricity is distributed from electrical substations to neighborhoods at 1.5×104 V . This is a 60Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120V that is delivered to your house.
Part A
How many turns does the primary coil on the transformer have if the secondary coil has 100 turns?
Express your answer using two significant figures. (nprim =?turns)

Part B
No energy is lost in an ideal transformer, so the output power Pout from the secondary coil equals the input power Pin to the primary coil. Suppose a neighborhood transformer delivers 280 A at 120 V. What is the current in the 1.5×104 V line from the substation?
Express your answer using two significant figures.

Answer 1

Answer:

Np=130 turns, Is=220 A

Explanation:

Part A:

Ns=100 turns

Vp= 1.5*104 V = 156 V

Vs= 120 V

As Np/Ns= Vp/Vs

⇒ Np= $\frac{Vp}{Vs}*Ns$

⇒Np=$\frac{156*100}{120}$

Np= 130 turns (It has two significant figures)

Part B

Is=280 A, Vs=120 V, Vp= 1.5*104 V= 156 V

For ideal transformer

Pin=Pout

Ip*Vp= Is*Vs

⇒Ip=($\frac{Is*Vs}{Vp}$)

⇒Ip=$\frac{280*120}{156}$

⇒Ip=215.4 A

to represent it as two significant figures we will write as

⇒Ip=220 A