Question

An AC adapter for a telephone-answering unit uses a transformer to reduce the line voltage of 120 V (rms) to a voltage of 9.0 V. The rms current delivered to the answering system is 400 mA. (a) If the primary (input) coil in the transformer in the adapter has 240 turns, how many turns are there on the secondary (output) coil? (b) What is the rms power delivered to the transformer? Assume an ideal transformer.

Answer 1

1. The number of turns on the secondary output is 18

2. The root mean square power delivered to the transformer is 48 Watts.

Step-by-step explanation:

A transformer is an electronic device that can be used for increasing or decreasing the value of a given voltage. It consists of primary coils and secondary coil of a definte number of turns. When voltage flows in the primary coil, it induces voltage in the secondary coil. The two types are: step-up and step down transformers.

1. For a given transformer,

`(V_(s) )/(V_(p) )` =
`(N_(s) )/(N_(p) )`

where
`V_(s)` is the value of the induced voltage in the secondary coil,
`V_(p)` is he voltage in the primary coil, and
`N_(s)` is the number of turns of the secondary coil,
`N_(p)` is the number of turns in the primary coil.

From the question,

`V_(s)` = 9.0 V,
`V_(p)` = 120 V,
`N_(p)` = 240,
`N_(s)` = ?

So that,

`N_(s)` =
`(V_(s)*N_(p) )/(V_(p) )`

=
`(9 * 240)/(120)`

= 18

The number of turns on the secondary output is 18.

2.
`Power_(rms)` =
`I_(rms)` ×
`V_(rms)`

= 0.4 × 120

= 48 W

The rms power delivered to the transformer is 48 Watts.