The questions are on the transformers test. Take it under real conditions before reading the mark scheme.
Quick answer: An alternating current reverses direction regularly, and its rms value, V₀/√2 for a sine wave, gives the equivalent steady heating effect. This mark scheme gives the model answers and the marks for the 8 questions of the Physics 11-12 test on transformers, from defining rms to laminated core, with the equivalent answers to accept.
Award marks for method as well as for the final answer. Accept answers within rounding and follow through an earlier slip. Do not penalise a missing unit more than once in each question.
Level: Physics grades 11-12 (A Level · IB · Class 11-12) · Curriculum: A Level 3.7.5
Question 1 Defining rms (2 marks)
The rms current is the value of steady direct current that would dissipate the same mean power in a resistor as the alternating current.
Marking: 1 mark for steady dc equivalent, 1 mark for same mean power in a resistor.
Question 2 Peak to rms (2 marks)
Vrms = V₀ / √2 = 340 / 1.414 = 240 V.
Marking: 1 mark for the formula, 1 mark for the answer.
Question 3 Power in a resistor (3 marks)
Vrms = 18 / √2 = 12.73 V. P = Vrms² / R = 162 / 12 = 13.5 W.
Marking: 1 mark for rms, 1 mark for P = V²/R, 1 mark for the answer.
Question 4 Transformer turns (3 marks)
a) Ns = Np Vs/Vp = 800 × 11.5 / 230 = 40 turns.
b) Is = 23 / 11.5 = 2.0 A; Ip = 23 / 230 = 0.10 A.
Marking: a) 1 mark. b) 1 mark for each current.
Question 5 Why high voltage? (3 marks)
For a given power P = VI, a higher voltage means a smaller current. The heat loss in the cables is I²R, so it falls with the square of the current. Less energy is wasted, and thinner, cheaper cables can be used. Transformers allow the voltage to be raised and lowered efficiently.
Marking: 1 mark for lower current, 1 mark for I²R, 1 mark for reduced loss or cost.
Question 6 Reading a trace (3 marks)
a) Two cycles take 10 ms, so T = 5.0 ms and f = 1/0.0050 = 200 Hz.
b) Vrms = 6.0 / √2 = 4.2 V.
Marking: a) 1 mark for T, 1 mark for f. b) 1 mark.
Question 7 Efficiency (2 marks)
Efficiency = 235 / 250 = 94 %.
Marking: 1 mark for the ratio, 1 mark for the percentage.
Question 8 Laminated core (2 marks)
Build the core from thin laminated sheets separated by insulation. This breaks up the loops in which eddy currents flow, so smaller currents flow and less energy is converted to heat.
Marking: 1 mark for laminations, 1 mark for the reason.
