Resonant transformer - sign of the voltage reinduced in the secondary winding

Resonant transformer - sign of the voltage reinduced in the primary winding

Consider a biresonant transformer with a small coupling coefficient k << 1.
Let the voltage applied to the primary LC circuit of a resonant transformer be
U1(t) = U*sin(2*Pi*t), - then the current through the primary caused by the
sinusoidal voltage U1(t) will also be sinusoidal: I1(t)=I*sin(2*Pi*t), and so will
be the corresponding flux. So the voltage U2(t) induced in the secondary winding
will be a positive multiple of -cos(2*Pi*t) and so will be the current I2(t) through
the secondary winding. But then the voltage U1,2(t) reinduced in the primary
winding by I2(t) should be a positive multiple of -sin(2*Pi*t), which has the opposite sign
to U1(t). So the voltage reinduced in the primary winding should conteract the flow
of the current through the primary winding. As far as I know the reinduced voltage
increases the current flowing through the primary winding. What is the explanation?

This is similar to a shorted winding on a transformer. (An air-core transformer is just like a normal transformer, but with a small coupling coefficient k). If you apply a voltage to the primary while leaving the secondary open, current will only flow through the magnetizing inductance. However, if you short-circuit the secondary, the shorted secondary will reflect a low-impedance path and lots of current will flow (in both the primary and secondary). In your case, since k is small, shorting the secondary won't cause quite as much current to flow as a normal transformer; but you will see the effect nonetheless.

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ZekeR said:

This is similar to a shorted winding on a transformer.... In your case, since k is small, shorting the secondary won't cause quite as much current to flow as a normal transformer; but you will see the effect nonetheless.

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I think the current reinduced in the primary will actually decrease, but the effective inductance of the primary will be different from its self-inductance.