Current Ratio

In the transformer of Fig. 6-4, the instantaneous primary current and instantaneous load current are designated as i₁ and i_L. The instantaneous primary current i₁ is shown entering the marked terminal of the primary Winding, and the instantaneous load current i_L is shown leaving the marked

terminal of the secondary winding. However, it is conventional, when writing the equations for two or more circuits that are coupled magnetically, to assume the instantaneous currents are flowing simultaneously either all into or all out of the marked terminals of the various coupled circuits. Thus, in a two-winding transformer, if the instantaneous primary and secondary currents flowing into the marked terminals are both positive or both negative, each of the two currents acting by itself would magnetize the core in the same direction, i.e., the mmfs of the two windings would be additive. Therefore, in accordance with this convention, the instantaneous secondary current i₂ is shown flowing into the marked terminal of the secondary of the transformer in Fig. 6-4, whereas the instantaneous load current i_L is shown flowing out of the marked secondary terminal. This means that i₂ and i_L are equal and opposite, and we have

iL = -i2

[6-15]

The relationship between these currents can be readily established on the basis that the exciting current in the ideal transformer is zero. Further, the capacitances between windings, between the windings and the core and tank, and between the turns of a winding can usually be neglected in the case of audio-frequency range transformers because the capacitive currents at these frequencies are generally small in relation to the rated current. Hence, capacitance effects in the windings of the ideal transformer are neglected.

Since the exciting current in an ideal transformer is zero, the permeability of the core in an ideal transformer must be infinite. This means that the net mmf of the windings must be zero under load as well as at no load. Therefore, the mmfs of the two windings resulting from the currents as shown in Fig. 6-4 must be equal, and we have for the ideal transformer

giving a current ratio of

[6-16]

The current ratio of the ideal transformer is therefore N₂/N₁ , and if the current phasors I₁ and I_L are used, we have

[6-17]

The current phasors I₁ and I_L in the ideal transformer are in phase with each other in accordance with the directions assumed in Fig. 6-4. Generally, when writing coupled-circuit equations, the instantaneous secondary current

i₂ is shown flowing into the marked side of the secondary winding at the same instant that the instantaneous primary current i₁ flows into the marked side of the primary winding. This means that the current i_L = -i₂, and that the phasor I₂ is 180° out of phase from the phasors I_L and I₁.