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.
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