Lecture20_Kim - Lecture 20-1 Transformers (1) When using or...

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Lecture 20-1 1 Transformers (1) When using or generating electrical power, high currents and low voltages are desirable for convenience and safety When transmitting electric power, high voltages and low currents are desirable – The power loss in the transmission wires goes as P = I 2 R – Assume we have 500 MW of power to transmit – If we transmit at 750 kV , the current would be 667 A (U=IV) – If the resistance of the power lines is 200 , the power dissipated in the power lines is 89 MW • 18% loss – Suppose we transmit at 375 kV instead 75% loss The ability to raise and lower alternating voltages would be very useful in everyday life
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Lecture 20-2 2 Transformers (2) We use a transformer to transform alternating currents and voltages from high to low or from low to high A transformer consists of two sets of coils wrapped around an iron core as illustrated Consider the primary windings with N P turns connected to a source of emf We can assume that the primary windings act as an inductor The current is out of phase with the voltage and no power is delivered to the transformer is delivered to the trans max sin emf V V t
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Lecture 20-3 3 Transformers (3) Now consider the second coil with N S turns The time-varying emf in the primary coil induces a time- varying magnetic field in the iron core. This core passes through the secondary coil Because both the primary and secondary coils experience the same changing magnetic field, we can write Thus a time-varying voltage is induced in the secondary coil described by Faraday’s Law B emf d VN dt  SS P SP P S P V VV N N N , B PP d dt B d dt   12 , PS V V V V  step-up step-down P S P S N N V V    P S P S N N V V   
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Lecture 20-4 Transformers (4) If we now connect a resistor R across the secondary windings, a current will begin to flow through the secondary coil (switch is closed) The power in the secondary circuit is then P S = I S V S Energy conservation: the power produced by the emf source in the primary coil will be transferred to the secondary coil, so we can write S P P P P S S S S P S P SP N V P I V P I V I I V V VN S I 2
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This note was uploaded on 12/07/2011 for the course PHYS 241 taught by Professor Wei during the Fall '08 term at Purdue University-West Lafayette.

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Lecture20_Kim - Lecture 20-1 Transformers (1) When using or...

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