PHY2049ch31D-32A%2811-4-09%29

# PHY2049ch31D-32A%2811-4-09%29 - Transformers (last part of...

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Transformers (last part of Ch.31) md sin( t) ξ=ξ ω The applied AC emf in the primary causes an induced emf, ξ turn , in each turn of the primary coil surrounding the iron core. With N P the number of turns on the primary side, The total induced voltage developed across the primary is, Pt u r n P VN = ξ The iron core causes the induced magnetic flux to circle around the rectangular core so that the same magnetic flux appears on the secondary side. With N S the number of turns on the secondary side, the total induced voltage developed across the secondary coil is, St u r n S = ξ

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Since the magnitude of the changing flux is equal on the two sides ξ turn is the same so, S P turn SP V V N N ξ= = But then, S P N VV N = So the voltage in the secondary can be increased or decreased by the turns ratio N S /N P ! Conservation of energy requires that, SS PP IV = P P P S P P VVN II I I N VN V N == =
So the current in the secondary is decreased or increased by the ratio N P /N S (the inverse of the previous ratio for the voltage in the secondary). P SP S N II N = If the secondary voltage is boosted up, the secondary current goes down, and visa versa (there is no free lunch). Such transformers provides the means by which the voltage produced at generation stations is stepped up for high voltage transmission over long distances (reducing the I 2 R losses) and then stepped down again to be used in homes and buildings.

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We now ask, for a purely resistive load, what effective resistance the primary sees for a given resistance on the secondary. If the resistive load were connected directly to the power supply and we did not know its resistance, we could determine it by measuring the current since then by Ohm’s law, V P = I P R, and we would have, R P P V R I = This provides our strategy for finding the effective resistance “seen” by the power supply due to the resistive load on the secondary.
With the switch is closed the current in the secondary is, S SS S V IV I R R =→ = P SP S N VI R N = Using P S N II N = But from above, S P N VV N = S P PP PS N N R NN = So 2 VN R IN ⎛⎞ = ⎜⎟ ⎝⎠ 2 eq RR == so,

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2 P eq S N RR N ⎛⎞ = ⎜⎟ ⎝⎠ allows another common use for transformers: impedance matching If we want to transfer the maximum energy from a source to a resistive load, it turns out that the energy transfer is maximized when the source resistance equals the load resistance . We show this for a direct current circuit. This expression
Recall our model for a real power supply has an internal resistance, r, so if we attach a load resistance, R , to this our circuit was modeled as shown here.

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## This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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PHY2049ch31D-32A%2811-4-09%29 - Transformers (last part of...

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