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Ideal single-phase step-down transformer U₁/U₂ = 2400/120V. The machine is connected to the grid electricity with a voltage of 2.6 kV. From the sine shape at this time, the steel core is (f = 0.09sin(314t) ) Wb. Determine the number of loops of the primary and secondary wires.

A. Primary: 500 loops, Secondary: 25 loops
B. Primary: 1000 loops, Secondary: 50 loops
C. Primary: 250 loops, Secondary: 12.5 loops
D. Primary: 125 loops, Secondary: 6.25 loops

User Misagh
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Final answer:

The correct number of loops for an ideal step-down transformer with a voltage ratio of 2400/120V, but operating at a grid voltage of 2.6 kV, is 500 primary loops and 25 secondary loops, reflecting a 20:1 turns ratio in accordance with the ratio of primary to secondary voltage.

Step-by-step explanation:

To determine the number of loops (or turns) in the primary and secondary windings of a step-down transformer, we use the transformer's voltage ratio and the formula relating the primary and secondary voltages to the number of turns in their respective windings: Vp/Vs = Np/Ns (where Vp and Vs are the primary and secondary voltages, and Np and Ns are the number of primary and secondary turns, respectively).

Given the ideal transformer has a rated voltage ratio of 2400/120V, but it is connected to a grid voltage of 2.6 kV (or 2600V), we adjust the voltage ratio according to the actual primary voltage. We do this by keeping the turns ratio (Np/Ns) constant while calculating Np and Ns with the actual voltage.

The actual turns ratio, based on the grid connection, would be 2600V/120V. Using the given standard ratio of 2400/120V and simplifying, we get a turns ratio of 20:1, which means that for every 20 turns on the primary, there is 1 turn on the secondary.

Option A (Primary: 500 loops, Secondary: 25 loops) reflects a turns ratio of 20:1. Since the other options (B, C, and D) do not reflect this ratio, they can be eliminated. Therefore, the calculation for the desired number of turns would be:

  • Primary: 500 loops
  • Secondary: 25 loops

User Arseniyandru
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