The sine wave, the DC generator and the transformer
Answers are for parents and teachers.
1
A generator turns at 3000 turns per minute and its peak emf is 50 V. Find f, T and the effective emf.
3000 ÷ 60 = 50 turns per second, so f = 50 Hz and T = 1 ÷ 50 = 0.02 s. Eeff = 0.707 × 50 = 35.4 V.
2
A resistor of 55 Ω is joined to a supply of 220 V effective. Find the effective current, the average power and the peak current.
Ieff = 220 ÷ 55 = 4 A. P = Ieff² R = 4² × 55 = 880 W. Imax = 4 ÷ 0.707 = 5.66 A.
3
A coil with a split-ring commutator turns at 25 turns per second. How many humps of current are there per second, and does the current in the outside circuit ever change direction?
2 humps per turn: 25 × 2 = 50 per second. The current never changes direction, because the brushes swap halves just as the coil’s emf reverses.
4
A step-down transformer has Np = 1800, Ns = 90 and Vp = 220 V. Find Vs. If Is = 6 A, find Ip and the power (ideal transformer).
Vs = 220 × 90 ÷ 1800 = 11 V. Ip = 6 × 90 ÷ 1800 = 0.3 A. Power = 11 × 6 = 66 W = 220 × 0.3 W.
5
A transformer has Np = 100 and Ns = 1000. Its primary is joined to an alternating supply of 9.0 V effective. Find Vs. What does the secondary show if the primary is joined to a steady 9.0 V cell instead, after the first instant, and why?
Vs = 9.0 × 1000 ÷ 100 = 90 V. With the steady cell the secondary shows 0 V after the first instant, because a steady current makes a steady flux, and only a changing flux induces an emf.