A transformer is a static electrical device that transfers electrical energy from one circuit to another without changing the frequency. Before entering into the actual topic of the working principle of a transformer, let us recall our knowledge of Faraday’s Law of Electromagnetic Induction. This famous law states that when a changing flux links with a conductor, a voltage is induced across the conductor, and the value of this voltage is directly proportional to the rate of change of flux linkage with respect to time.
Now, we shall examine how, from this basic law of induction, a transformer is developed. Let’s take a coil and supply it with an alternating source. We know that when a current flows through a coil, a magnetic field is developed in and around the coil. Naturally, flux will also be developed in and around the coil, as shown. This flux is also alternating, as the current through the coil is alternating. If the current from the source varies with a sinusoidal wave, the flux in and around the coil also varies sinusoidally.
Now, consider another coil nearby. This changing flux will link with the second coil. Therefore, according to Faraday’s Law of Electromagnetic Induction, a voltage—or better to say, an emf—is developed across the second coil. If the circuit connected to the second coil is closed, there will be a current flowing through it. So, we can conclude that a portion of energy from the source has been transferred to the second coil circuit without any direct electrical connection. This is the most basic working principle of a transformer.
Now, we shall develop a basic transformer from this setup for better understanding. Here, you observed that the second coil links with only a small portion of the flux generated by the first coil. Hence, this arrangement transfers only a small portion of source energy. If we need to transfer the entire energy supplied to the first coil, we need to link the entire flux with the second coil. For that, we obviously need to put a low reluctance path between the first and second coils. We do this by using a closed core made of magnetic material like steel. Both the coils surround the core. As soon as we place the core, the entire flux is confined within it and will therefore fully link with the second coil.
In a simple transformer, we refer to the first coil as the primary winding and the second coil as the secondary winding. Now, we connect an alternating source across the primary winding. An alternating current starts flowing through the primary winding. As a result, a changing flux is developed in the iron core. This flux is in phase with the input current.
Now, as per Faraday’s Law of Electromagnetic Induction, the emf induced in each conductor of the secondary winding is directly proportional to the rate of change of flux linkage. If there are \(N_2\) turns in the secondary winding, the total induced emf across the winding will be \(N_2\) times the emf per turn. If we express the flux with a sinusoidal wave, the emf will be a cosine wave, as this is the derivative of the flux function. So, this emf will lag the flux by 90 degrees.
We can observe that the same flux links with the primary winding too; therefore, the same emf is induced per turn in the primary winding. Since the same changing flux links both windings, the same rate of change of flux applies to both. If the number of turns in the primary winding is \(N_1\), the total induced emf across it will be \(N_1\) times the emf per turn. As the source is connected across the primary winding, according to Kirchhoff’s Voltage Law, the induced emf is equal and opposite to the source voltage. Since the source voltage and primary induced voltage are equal and opposite, ideally no current is drawn from the source. However, to maintain magnetization, the winding takes a small current. This small current is called the magnetizing current.
Until now, we have not connected any load across the secondary winding. If we now connect a load, as there is already a voltage induced across the secondary winding, a current starts flowing through the load as well as the secondary winding. This current is called the secondary current. Due to this current, another flux is developed in the core. This flux opposes the main magnetic flux. This means it will try to reduce the main magnetic flux. But if the main flux decreases, the magnetic balance of the system will be disturbed. Therefore, the system tries to keep the magnetic flux constant. To do so, the system has to cancel out the additional flux generated by the secondary. This is done by drawing extra current from the source. The primary winding draws extra current to produce a counter flux that cancels the secondary flux. Thus, the net flux in the core remains constant—only the magnetizing flux.
The flux produced by a coil is directly proportional to the number of turns and the current in the coil. Since the primary and secondary fluxes are equal, the primary and secondary currents are inversely proportional to the number of turns. Also, the induced voltage across a winding is directly proportional to the number of turns. From these two relationships, we can conclude that the product of current and voltage for both windings is ideally the same. That also means, ideally, the power taken from the source is delivered to the load.
This simple system of two windings linked by a magnetic core is the most basic model of a transformer. Here, you see that for a certain power output, both voltage and current in the secondary circuit depend on the number of turns in the secondary winding. If the number of turns in the secondary is greater than in the primary, the output voltage is greater than the source voltage, and the secondary current is less than the source current. This is called a step-up transformer. If the number of turns in the secondary is less, the output voltage is lower, and the current is higher. This is called a step-down transformer.
So, finally, we can say: a transformer is a static machine that transfers electrical power from the source circuit to the load circuit without changing the frequency, though the voltage and current levels may differ.