#### Quiz

Q1) In a transformer, electrical power is transferred from one circuit to another without change in

A. Voltage.

B. Current.

C. Frequency.

D. Turns.

Answer) C.

Q2) Flux linkage between primary and secondary windings of a transformer is proportional to which of the following?

A. Cross sectional area of the core and the length of the flux path.

B. Cross sectional area and Permeability of the core

C. Cross sectional area and Reluctance of the core.

D. Permeability of the core and the length of the flux path.

A. Voltage.

B. Current.

C. Frequency.

D. Turns.

Q2) Flux linkage between primary and secondary windings of a transformer is proportional to which of the following?

A. Cross sectional area of the core and the length of the flux path.

B. Cross sectional area and Permeability of the core

C. Cross sectional area and Reluctance of the core.

D. Permeability of the core and the length of the flux path.

Answer) B.

####

#### Transformer Principle of Operation Simulation

When the next simulation is not visible, please refer to the following link.

####
**Transformers**

Consider a pair of coils, side by side, as shown in Figure 1. One is connected to a battery and the other is connected to a galvanometer.

It is customary to refer to the coil connected to the power source as the primary (input), and the other as the secondary (output). As soon as the switch is closed in the primary and current passes through its coil, a current occurs in the secondary also—even though there is no material connection between the two coils. Only a brief surge of current occurs in the secondary, however. Then when the primary switch is opened, a surge of current again registers in the secondary but in the opposite direction.

The explanation is that the magnetic field that builds up around the primary extends into the secondary coil. Changes in the magnetic field of the primary are sensed by the nearby secondary. These changes of magnetic field intensity at the secondary induce voltage in the secondary, in accord with Faraday’s law. If we place an iron core inside the primary and secondary coils of the arrangement shown in Figure 1, the magnetic field within the primary is intensified by the alignment of magnetic domains in the iron. The magnetic field is also concentrated in the core, which extends into the secondary, so the secondary intercepts more of the field change. The galvanometer will show greater surges of current when the switch of the primary is opened or closed.

Instead of opening and closing a switch to produce the change of magnetic field, suppose that alternating current is used to power the primary. Then the rate at which the magnetic field changes in the primary (and hence in the secondary) is equal to the frequency of the alternating current.

Now we have a transformer, as shown in Figure 2. A transformer is a device for increasing or decreasing voltage through electromagnetic induction. A transformer works by inducing a changing magnetic field in one coil, which induces an alternating current in a nearby second coil.

In its simplest form, an ac transformer consists of two coils of wire wound around a core of soft iron, like the apparatus for the Faraday experiment. The coil on the left in Figure 3 has $\ N_{1}$ turns and is connected to the input ac potential difference source. This coil is called the primary winding, or the primary.

The coil on the right, which is connected to a resistor R and consists of $\ N_{2}$ turns, is the secondary. As in Faraday’s experiment, the iron core “guides”the magnetic field lines so that nearly all of the field lines pass through both of the coils.

Because the strength of the magnetic field in the iron core and the crosssectional area of the core are the same for both the primary and secondary windings, the measured ac potential differences across the two windings differ only because of the different number of turns of wire for each. The applied voltage that gives rise to the changing magnetic field in the primary is related to that changing field by Faraday’s law of induction.

$\Delta V_{1}=-N_{1}\frac{\Delta \Phi_{M} }{\Delta t } $

Similarly, the induced voltage across the secondary coil is

$\Delta V_{2}=-N_{2}\frac{\Delta \Phi_{M} }{\Delta t } $

Taking the ratio of $\Delta V_{1}$ to $\Delta V_{2}$ causes all terms on the right side of both equations except for $\ N_{1}$ and $\ N_{2}$ to cancel. This result is the transformer equation.

Another way to express this equation is to equate the ratio of the potential differences to the ratio of the number of turns.

$\ \frac{\Delta V_{2}}{\Delta V_{1}}=\frac{N_{2}}{N_{1}}$

When $\ N_{2}$ is greater than $\ N_{1}$, the secondary voltage is greater than that of the primary, and the transformer is called a step-up transformer.When $\ N_{2}$ is less than $\ N_{1}$, the secondary voltage is less than that of the primary, and the transformer is called a step-down transformer. It may seem that a transformer provides something for nothing. For example, a step-up transformer can change an applied voltage from 10 V to 100 V.

However, the power output at the secondary is, at best, equal to the power input at the primary. In reality, energy is lost to heating and radiation, so the output power will be less than the input power. Thus, an increase in induced voltage at the secondary means that there must be a proportional decrease in current.

It is customary to refer to the coil connected to the power source as the primary (input), and the other as the secondary (output). As soon as the switch is closed in the primary and current passes through its coil, a current occurs in the secondary also—even though there is no material connection between the two coils. Only a brief surge of current occurs in the secondary, however. Then when the primary switch is opened, a surge of current again registers in the secondary but in the opposite direction.

*FIGURE 1. Whenever the primary switch is opened or closed, voltage is induced in the secondary circuit.*The explanation is that the magnetic field that builds up around the primary extends into the secondary coil. Changes in the magnetic field of the primary are sensed by the nearby secondary. These changes of magnetic field intensity at the secondary induce voltage in the secondary, in accord with Faraday’s law. If we place an iron core inside the primary and secondary coils of the arrangement shown in Figure 1, the magnetic field within the primary is intensified by the alignment of magnetic domains in the iron. The magnetic field is also concentrated in the core, which extends into the secondary, so the secondary intercepts more of the field change. The galvanometer will show greater surges of current when the switch of the primary is opened or closed.

Instead of opening and closing a switch to produce the change of magnetic field, suppose that alternating current is used to power the primary. Then the rate at which the magnetic field changes in the primary (and hence in the secondary) is equal to the frequency of the alternating current.

*FIGURE 2. A simple transformer arrangement using an iron core creates greater current in the secondary coil.*Now we have a transformer, as shown in Figure 2. A transformer is a device for increasing or decreasing voltage through electromagnetic induction. A transformer works by inducing a changing magnetic field in one coil, which induces an alternating current in a nearby second coil.

*Figure 3. A transformer uses the alternating current in the primary circuit to induce an alternating current in the secondary circuit*In its simplest form, an ac transformer consists of two coils of wire wound around a core of soft iron, like the apparatus for the Faraday experiment. The coil on the left in Figure 3 has $\ N_{1}$ turns and is connected to the input ac potential difference source. This coil is called the primary winding, or the primary.

The coil on the right, which is connected to a resistor R and consists of $\ N_{2}$ turns, is the secondary. As in Faraday’s experiment, the iron core “guides”the magnetic field lines so that nearly all of the field lines pass through both of the coils.

Because the strength of the magnetic field in the iron core and the crosssectional area of the core are the same for both the primary and secondary windings, the measured ac potential differences across the two windings differ only because of the different number of turns of wire for each. The applied voltage that gives rise to the changing magnetic field in the primary is related to that changing field by Faraday’s law of induction.

$\Delta V_{1}=-N_{1}\frac{\Delta \Phi_{M} }{\Delta t } $

Similarly, the induced voltage across the secondary coil is

$\Delta V_{2}=-N_{2}\frac{\Delta \Phi_{M} }{\Delta t } $

Taking the ratio of $\Delta V_{1}$ to $\Delta V_{2}$ causes all terms on the right side of both equations except for $\ N_{1}$ and $\ N_{2}$ to cancel. This result is the transformer equation.

TRANSFORMER EQUATION$\Delta V_{2}=\frac{N_{2}}{N_{1}} \Delta V_{1}$ |

Another way to express this equation is to equate the ratio of the potential differences to the ratio of the number of turns.

$\ \frac{\Delta V_{2}}{\Delta V_{1}}=\frac{N_{2}}{N_{1}}$

When $\ N_{2}$ is greater than $\ N_{1}$, the secondary voltage is greater than that of the primary, and the transformer is called a step-up transformer.When $\ N_{2}$ is less than $\ N_{1}$, the secondary voltage is less than that of the primary, and the transformer is called a step-down transformer. It may seem that a transformer provides something for nothing. For example, a step-up transformer can change an applied voltage from 10 V to 100 V.

However, the power output at the secondary is, at best, equal to the power input at the primary. In reality, energy is lost to heating and radiation, so the output power will be less than the input power. Thus, an increase in induced voltage at the secondary means that there must be a proportional decrease in current.