# Basic Transformer Question

My understanding of how a transformer works is that there is a primary and a secondary coil wrapped around a common iron coil. An alternating current in the primary coil results in a changing magnetic field which in turn results an induced current in the secondary coil.

The resulting voltage across secondary coil is proportional the the number of turns in the secondary coil. My understanding of this is that each loop produces a small emf and these loops are all in series so adding more loops is like adding more cells in series in a battery.

My question is why does adding more loops in the primary winding reduce the output voltage? In an electromagnet, increasing the number of turns of wire increases the magnetic field. So I would think that increasing the number of loops in the primary coil would result in a larger magnetic field and thus a greater induced voltage in the secondary coil.

We usually consider a transformer to be driven by a fixed voltage $$V_i$$.

The current in the primary is then determined by voltage and inductance $$V_i/L_i$$.

If you add turns to the primary, you increase the inductance, and therefore decrease the current. This decreased current makes less magnetic field. So the secondary produces less voltage.

• Right, that make sense. My mistake was thinking of the primary coil as if it were a DC electromagnet and not considering the (crucial) role that inductance plays. – M. Enns Jun 7 at 17:59

Let's see this in another way.

Inductance of a coil depends on loops a coil has and is proportional to number of loops a coil has.

As we also know the relation between Voltage and current for a coil is.

$$V=L*\frac{di}{dt}$$

Now if we consider that the source has a fixed supply power, we will get that an increase in number of loops in primary coil the inductance will increase.

As there is a increase in inductance we can say that there will be decrease in current flow leading to a smaller induced voltage in secondary coil.

Hence by adding more primary loops you are decreasing the flux produced.

This effect can be understood by comparing both of these two general formula.

$$VaNa=VbNb$$

$$\frac{Va}{Ia}=\frac{Vb}{Ib}$$

As we see voltages of both coils show direct relationships to currents flowing through them,While there is inverse relationships to the number of loops in coil ( This is because currents show inverse relationships to inductance or loops in a coil)

The resulting voltage across secondary coil is proportional the the number of turns in the secondary coil.

My question is why does adding more loops in the primary winding reduce the output voltage?

The problem with your reasoning is you are looking at each winding independent of the other and that you are looking only at the voltages and not the combination of voltage times current (power).

For an ideal transformer where power in equals power out, the subscripts $$p$$ and $$s$$ denote the primary and secondary, and N is the number of turns

$$V_{p}I_{p}=V_{s}I{s}$$

$$\frac{V_p}{V_s}=\frac{I_s}{I_p}=\frac{N_p}{N_s}$$

Hope this helps