An engineer in India (standard household voltage = 220 volts) is designing a transformer for use on her upcoming trip to Canada (standard household voltage = 120 volts). If her input coil has 240 turns, how many turns should her output coil have?
Answer (3)
he should a step-up transformer with k=220/120=1.83 so output coil must have 240*1.83=440 turns
The student is asking about designing a transformer for voltage conversion between India and Canada. To find the number of turns needed on the transformer's output coil (secondary coil) when converting from a 220 V system (India) to a 120 V system (Canada), we use the formula derived from Faraday's law of induction:
Vp/Vs = Np/Ns,
where Vp is the primary voltage, Vs is the secondary voltage, Np is the number of turns in the primary coil, and Ns is the number of turns in the secondary coil.
Given: Vp = 220 V (India) Vs = 120 V (Canada), Np = 240 turns (input coil).
We rearrange the formula to solve for Ns:
Ns = (Vs ร Np) / Vp,
Ns = (120 V ร 240 turns) / 220 V.
Performing the calculation:
Ns = (28,800 turnsยทV) / 220 V,
Ns = 131 turns (approximated to the nearest whole number).
Therefore, the engineer should use a secondary coil with approximately 131 turns for the transformer.
For a transformer with a primary coil of 280 turns and an input voltage of 240 V, the output coil should have 140 turns to produce an output voltage of 120 V. This relationship is established using the transformer turn ratio formula. Different output voltages can be calculated by substituting the respective values into the equation.
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