Q174 · Practice questionComplex familiar7 marks
QUESTION 174 (7 marks)
An ideal transformer has primary turns and secondary turns. It is connected to a rms AC supply. A connected load draws rms from the secondary.
a)[2 marks]
Calculate the secondary rms voltage.
b)[2 marks]
Calculate the primary rms current.
c)[3 marks]
A real transformer is connected to DC. Once its primary current is steady, explain why it does not sustain an induced secondary voltage.
WORKED SOLUTION
7 marksPractice marking scheme
ANSWER
(a) . (b) . (c) A steady primary current gives constant flux, hence zero continuing induced secondary EMF.
Worked solution
(a) , so .
(b) An ideal transformer conserves power: . Thus .
(c) AC produces a changing primary current and changing magnetic flux linking both coils. Faraday's law gives an induced EMF proportional to the rate of this flux change. Once a DC current is steady, the flux is constant and , so no sustained secondary EMF is induced. A brief switching transient is possible.
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Apply the turns-to-voltage ratio.
Part a: Calculate the secondary voltage.
Part b: Use equal input and output power for the ideal transformer.
Part b: Calculate the primary current.
Part c: Link changing primary current to changing shared flux.
Part c: Explain secondary induction using Faraday law.
Part c: Distinguish steady DC from a possible switching transient.
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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