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Elementary Theory of an Ideal Transformer

The basic theory of a transformer is not difficult to understand. To simplify matters as much as possible, let us first consider an ideal transformer, that is, one in which the resistance of the windings is negligible and the core has no losses.

Let the secondary be open (Fig. 15), and let a sine wave of potential difference

Fig. 15. Elementary diagram of an ideal transformer with an open secondary winding.

flow in the primary winding. Since the primary resistance is negligible and there are no losses in the core, the effective resistance is zero and the circuit is purely reactive. Hence the current wave im lags the impressed voltage wave Φ1 by 90 time degrees, as shown in Fig. 17. The reactance of circuit is very high and the magnetizing current is very small. This current in the N1 turns of the primary magnetizes the core and produces a flux Φ that is at all times proportional to the current (if the permeability of the circuit is assumed to be constant), and therefore in time phase with the current. The flux, by its rate of change, induces in the primary winding E1 which at every instant of time is equal in value and opposite in direction to V1 It is called counter e.m.f. of the primary. The value which the primary current attains must be such that the flux which it produces in the core is of sufficient value to induce in the primary the required counter e.m.f.

Figs. 16, 17. Current, voltage and flux curves of an ideal (no loss) transformer

Since the flux also threads (or links) the secondary winding a voltage e2 is induced in the secondary. This voltage is likewise proportional to the rate of change of flux and so is in time phase with e1 but it may have any value depending upon the number of turns N2 in the secondary.