An ideal step-down transformer is connected to a 2200 V primary line and delivers power to a 220 V load. If the primary winding has 4000 turns and the output power delivered to the load is 4.4 kW, what are the number of turns in the secondary coil and the primary current?
Answer and explanation
Correct answer: C. Ns = 400 turns, Ip = 2.0 A
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- Step 1: The transformer turn ratio equation relates voltages and turns: .
- Step 2: Given , , and :
- Step 3: For an ideal transformer (100% efficiency), input power equals output power: .
- Step 4: Since :
Answer
Ns = 400 turns, Ip = 2.0 A
Why not the others: 'Ns = 40,000 turns, Ip = 20.0 A' treats the step-down transformer as a step-up transformer (); 'Ns = 400 turns, Ip = 20.0 A' calculates secondary current instead of primary current; 'Ns = 40 turns, Ip = 2.0 A' divides by 100 instead of 10.
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