QP 26 A transformer' is nothing more than two inductors coupled by a mutual inductance M. An ideal transformer maximizes

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Qp 26 A Transformer Is Nothing More Than Two Inductors Coupled By A Mutual Inductance M An Ideal Transformer Maximizes 1 (61.39 KiB) Viewed 29 times

QP 26 A transformer' is nothing more than two inductors coupled by a mutual inductance M. An ideal transformer maximizes M by making sure that all of the magnetic field lines which pass through one inductor also pass through the other. Typically the transformer consists of two coils of wire (the inductors) wound on a single toroidal iron core. Let the "primary' winding have N, turns and a self-inductance L, and the secondary' winding have N. turns and a self-inductance L. You may assume the coils to have zero resistance. Ne, Lup Nsts a) A sinusoidal voltage of amplitude V, is applied to the primary winding, Determine the amplitude of the voltage V, across the secondary winding. b) Find the mutual inductance M of this ideal transformer. Express your results in terms of the variables given above. Now suppose a sinusoidal voltage Vcos(cot) is applied to the primary and a load' resistor Ris connected across the secondary. Currents will flow in both the primary and secondary circuits. Let the amplitude of these currents be I, and I., respectively, Veslot) If the load resistance R in the secondary circuit is not too large (how large need not concern us here), the transformer acts as a perfect conveyor of electrical power from the primary to the secondary. In other words, IV = 1V.. c) Find I, and I, in terms of the voltage applied to the primary and the number of tums, N, and N. in the primary and secondary windings. d) Find the peak power dissipation in the load resistor R. By what factor, if any, does it differ from the power dissipation that would occur if the transformer were omitted and the resistor connected directly to the voltage source? Finally, suppose a resistor Re is inserted into the primary circuit, in series with the primary winding. (We assume these resistances are both sufficiently small that the idealized conditions set out above remain correct.) Ro m V, coskot) e) For this new circuit again find the peak power dissipation in the load resistor R. Express your result in terms of the drive voltage amplitude V, N, N, and R. Prove that the power is maximized when N/N, - (R/R.) Evaluate this maximum power. This problem illustrates the concept of impedance matching,