Question

A note about rms, which stands for root-mean-square: The rms voltage is a measure of the average effective voltage. If you use peak (maximum) values of voltage or current in any of the transformer equations, you get peak values out. If you use rms values in the equations, you get rms values out. The bottom line: Don't be confused by the rms values—you can use them in the equations and you'll be fine.

A typical pole-mounted transformer, the last step in the power distribution process before electricity is delivered to residential customers, has an rms voltage of 9600 volts on the primary coil. The secondary coil has an rms output voltage of 240 volts, which is delivered to one or more houses.

a. What is the ratio of the number of turns in the primary coil to the number in the secondary?
b. If the rms current on the primary side is 4.00 A, and each house requires an rms current of 40 A, how many houses can this transformer supply electricity to?

Answer 1

a. ratio = 40

b. 4 houses can be supplied

Step-by-step explanation:

Relations in a Transformer

The pole-mounted transformers are mainly used to lower higher distribution voltages to residential-level voltages. It is done by using a combination of primary and secondary coils so the relation or ratio is correctly achieved.

a. The ratio between the number of turns in the primary coil to the secondary coil is

`\displaystyle r=(n_1)/(n_2)=(V_1)/(V_2)=(9600)/(240)=40`

b. This ratio also applies to the primary and secondary currents, being the secondary current r times the primary current.

The ratio between the currents is given by

`\displaystyle r=(n_1)/(n_2)=(i_2)/(i_1)=40`

We can know the secondary current

`i_2=40* i_1=40* 4=160\ A`

Given each house requires 40 A rms, we can supply electricity to 160/40=4 houses