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Question
A 200V/120V step-down transformer of 90% efficiency is connected to an induction stove of resistance 40 Ω. Find the current drawn by the primary of the transformer.
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Solution
Given data:
Vp = 200 V
Vs = 120 V
η = 90% = `90/100` = 0.9
`η = "output power"/"input power"`
`therefore 0.9 = ("V"_"S""I"_"S")/("V"_"p""I"_"p")`
`therefore "V"_"S" = "I"_"S""R"_"S"`
`"I"_"S" = "V"_"S"/"R"_"S" = 120/40` = 3A
∴ 0.9 = `(120 xx 3)/(200 xx "I"_"p")`
`"I"_"p" = (120 xx 3)/(200 xx 0.9) = (120 xx 3)/(20 xx 9)`
`"I"_"p"` = 2 A
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