Physics quiz question: transformer power input

Physics 205B Quiz 6, spring semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 20.37

A physics question on an online discussion board[*] was asked:

I have an alternating current supply of 6.0 V and want to make a step-up transformer to get 120 V. It should output a maximum 300 mA of current.

The amount of power input on the primary should be:
(A) 0.015 W.
(B) 6.0 W.
(C) 1.8 W.
(D) 36 W.

[*] answers.yahoo.com/question/index?qid=20080623073346AAOZxW8.

Correct answer (highlight to unhide): (D)

The transformer equations are:

ε₂/ε₁ = N₂/N₁ = I₁/I₂,

where the input (alternating root-mean-square) voltage is ε₁ = 6.0 V, and the output (alternating rms) voltage and current are ε₂ = 120 V and I₂ = 0.300 A, respectively. Noting that power P is the product of the (rms) current and voltage values, and that for an ideal transformer power is conserved, then:

ε₂/ε₁ = I₁/I₂,

I₂·ε₂ = I₁·ε₁,

I₂·ε₂ = P₁,

(0.300 A)·(120 V) = 36 W = P₁,

is the power input (and output) of this transformer.

Response (A) is I₂·ε₁/ε₂; response (B) is the input (rms) current value I₁ = I₂·ε₂/ε₁; response (C) is I₂·ε₂
.
Sections 30882, 30883
Exam code: quiz06Lp4s
(A) : 6 students
(B) : 5 students
(C) : 15 students
(D) : 11 students

Success level: 30%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.35