Electromagnetic Induction
4 marks · NormalA power station supplies 20,000 V a.c. at a current of 800 A to a step-up transformer which is 100% efficient. The transformer increases the voltage for long-distance transmission. A second transformer later steps the voltage down to 5,000 V for use in a factory.
Calculate the output current from the step-up transformer if the transmission voltage is increased to 100,000 V.
Calculate the current supplied to the factory after the voltage is stepped down to 5,000 V, assuming 100% efficiency throughout.
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(a) 160 A
(b) 3200 A
Common mistakes: using voltage ratio instead of power equation
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Sets up correct power equality equation: .
A1 (a) · 1 mark · Correct calculation: 160 A. (follow-through)
M1 (b) · 1 mark · Uses correct power equality: . (follow-through)
A2 (b) · 1 mark · Correct value: 3200 A. (follow-through)
Worked solution
a) For a 100% efficient transformer:
b) Input power at the second transformer: . Let current at 5,000 V be .