Current direction in full-wave rectifier circuit during positive half-cycle

Question

^{simulate this circuit – Schematic created using CircuitLab}

'Microelectronics' by Sedra and Smith describes the behaviour of the above circuit (image taken from book): a transformer with an AC supply on its primary winding and a centre-tapped secondary winding with a rectifier.

It says that diode D1 conducts during the positive half-cycle while diode D2 is off. In the negative half-cycle, the opposite happens.

My question is regarding the direction of the secondary circuit's current. In up to period T/4, current will be increasing in the primary and magnetic flux will be increasing in the secondary winding. So current will flow through D1.

But from period T/4 to T/2, current will be decreasing in the primary, so magnetic flux will decrease in the secondary winding. According to Lenz's Law, shouldn't the direction of current in the secondary now be opposite to its direction in period 0 to T/4?

I mean, we are getting two opposite directions of current during the same positive half-cycle. But why this is not happening? Why we are getting same current direction in positive half cycle?

Answer 1

up to period T/4 current will be increasing in 'transformer primary', so magnetic flux will be increasing in 'transformer secondary'

and

from period T/4 to T/2 current will be decreasing in 'transformer primary', so magnetic flux will be decreasing in 'transformer secondary'.

It seems that the whole premise of your question assumes that secondary current creates a flux in the transformer core. This is incorrect because any flux created by secondary current is wholly cancelled by the opposite current (divided by the turns ratio) in the primary.

The only flux in the transformer is from the applied voltage and the inductance of the primary.

Load currents do not add or subtract flux.

If (in another universe) they did add or subtract flux then we could never get a transformer to work (due to subtraction of flux) or, that alternative universe would self-destruct due to induction runaway (if fluxes added).

Answer 2

You're mixing up your currents and voltages. Depending on the load applied on the secondary, the phase relationship between voltage and current changes.

Let's say we have an AC voltage applied to our primary side that has the shape of sin(t). Since the primary coil is an inductor, we know that the current in the primary will be behind the voltage by 90 degrees. Therefore we know that primary current will look like cos(t).

We know from faraday's law that the magnetic flux is directly proportional to the current flowing in the conductor, therefore the magnetic flux will be in-phase with the current in the primary. So it will look like cos(t) also.

Now for the tricky bit. Faradays law states that the voltage generated in a conductor is equal to the negative of the differential of the magnetic flux. So our voltage will look like -(differential(cos(t))). Which gives us -(-sin(t)) = sin(t). There are two things to note here, 1) We have the secondary the same polarity/in phase with the primary and 2) Faraday's law of induction only describes voltage.

So this is where your confusion is coming from, the reason we don't get two opposite current directions in the same half cycle is that faraday's law is describing the voltage generated in the secondary, not the current. Lenz' law is useful to try and determine what direction the current will be flowing as a result of this voltage.