# The relationship between voltage and current in a transformer

### RELATIONSHIP BETWEEN PRIMARY AND SECONDARY WINDINGS

As just explained, the turns ratio of a transformer affects current as well as voltage . If voltage is doubled in the secondary, current is halved in the secondary. A transformer needs an alternating current that will create a changing magnetic field. The ratio between the voltages in the coils is the same as the ratio of the. Assuming that the transformer is % efficient (no energy is lost between its primary coil and Ip is the current in the primary coil in amperes (amps), A.

Copper loss can be minimized by using the proper diameter wire. Large diameter wire is required for high-current windings, whereas small diameter wire can be used for low-current windings. Eddy-Current Loss The core of a transformer is usually constructed of some type of ferromagnetic material because it is a good conductor of magnetic lines of flux.

Whenever the primary of an iron-core transformer is energized by an alternating-current source, a fluctuating magnetic field is produced. This magnetic field cuts the conducting core material and induces a voltage into it. The induced voltage causes random currents to flow through the core which dissipates power in the form of heat. Since the thin, insulated laminations do not provide an easy path for current, eddy-current losses are greatly reduced.

Hysteresis Loss When a magnetic field is passed through a core, the core material becomes magnetized. To become magnetized, the domains within the core must align themselves with the external field.

If the direction of the field is reversed, the domains must turn so that their poles are aligned with the new direction of the external field. Power transformers normally operate from either 50 Hz, or Hz alternating current. Each tiny domain must realign itself twice during each cycle, or a total of times a second when 50 Hz alternating current is used.

The energy used to turn each domain is dissipated as heat within the iron core. Hysteresis loss can be held to a small value by proper choice of core materials. The input power is equal to the product of the voltage applied to the primary and the current in the primary. The output power is equal to the product of the voltage across the secondary and the current in the secondary. The difference between the input power and the output power represents a power loss.

You can calculate the percentage of efficiency of a transformer by using the standard efficiency formula shown below: If the input power to a transformer is watts and the output power is watts, what is the efficiency? Hence, the efficiency is approximately The voltage, current, and power-handling capabilities of the primary and secondary windings must also be considered.

The maximum voltage that can safely be applied to any winding is determined by the type and thickness of the insulation used. When a better and thicker insulation is used between the windings, a higher maximum voltage can be applied to the windings.

The maximum current that can be carried by a transformer winding is determined by the diameter of the wire used for the winding. If current is excessive in a winding, a higher than ordinary amount of power will be dissipated by the winding in the form of heat.

This heat may be sufficiently high to cause the insulation around the wire to break down. If this happens, the transformer may be permanently damaged. The power-handling capacity of a transformer is dependent upon its ability to dissipate heat.

If the heat can safely be removed, the power-handling capacity of the transformer can be increased.

### BBC - GCSE Bitesize Science - Transformers : Revision, Page 4

This is sometimes accomplished by immersing the transformer in oil, or by the use of cooling fins. The power-handling capacity of a transformer is measured in either the volt-ampere unit or the watt unit.

Two common power generator frequencies 50 hertz and hertz have been mentioned, but the effect of varying frequency has not been discussed.

If the frequency applied to a transformer is increased, the inductive reactance of the windings is increased, causing a greater ac voltage drop across the windings and a lesser voltage drop across the load. However, an increase in the frequency applied to a transformer should not damage it. But, if the frequency applied to the transformer is decreased, the reactance of the windings is decreased and the current through the transformer winding is increased. If the decrease in frequency is enough, the resulting increase in current will damage the transformer.

For this reason a transformer may be used at frequencies above its normal operating frequency, but not below that frequency. A brief discussion of some of these applications will help you recognize the importance of the transformer in electricity and electronics. These transformers have two or more windings wound on a laminated iron core.

The number of windings and the turns per winding depend upon the voltages that the transformer is to supply. Their coefficient of coupling is 0. You can usually distinguish between the high-voltage and low-voltage windings in a power transformer by measuring the resistance. The low-voltage winding usually carries the higher current and therefore has the larger diameter wire.

This means that its resistance is less than the resistance of the high-voltage winding, which normally carries less current and therefore may be constructed of smaller diameter wire.

## Transformers - Higher tier

So far you have learned about transformers that have but one secondary winding. The typical power transformer has several secondary windings, each providing a different voltage. The schematic symbol for a typical power-supply transformer is shown in figure This proportion also shows the relationship between the number of turns in each winding and the voltage across each winding. This proportion is expressed by the equation: Notice the equation shows that the ratio of secondary voltage to primary voltage is equal to the ratio of secondary turns to primary turns.

The equation can be written as: The following formulas are derived from the above equation: If any three of the quantities in the above formulas are known, the fourth quantity can be calculated.

A transformer has turns in the primary, 50 turns in the secondary, and volts applied to the primary Ep. What is the voltage across the secondary E s? There are turns of wire in an iron-core coil. If this coil is to be used as the primary of a transformer, how many turns must be wound on the coil to form the secondary winding of the transformer to have a secondary voltage of one volt if the primary voltage is five volts?

The ratio of the voltage 5: Sometimes, instead of specific values, you are given a turns or voltage ratio. In this case, you may assume any value for one of the voltages or turns and compute the other value from the ratio. For example, if a turn ratio is given as 6: The transformer in each of the above problems has fewer turns in the secondary than in the primary.

As a result, there is less voltage across the secondary than across the primary. The ratio of a four-to-one step-down transformer is written as 4: A transformer that has fewer turns in the primary than in the secondary will produce a greater voltage across the secondary than the voltage applied to the primary.

### BBC - GCSE Bitesize: Transformers - Higher tier

A transformer in which the voltage across the secondary is greater than the voltage applied to the primary is called a STEP-UP transformer. The ratio of a one-to-four step-up transformer should be written as 1: Notice in the two ratios that the value of the primary winding is always stated first.

The magnetic field produced by the current in the secondary interacts with the magnetic field produced by the current in the primary. This interaction results from the mutual inductance between the primary and secondary windings.

• Conservation of energy in transformers

It is also the means by which energy is transferred from the primary winding to the secondary winding. The inductance which produces this flux is also common to both windings and is called mutual inductance.

Figure 11 shows the flux produced by the currents in the primary and secondary windings of a transformer when source current is flowing in the primary winding. When a load resistance is connected to the secondary winding, the voltage induced into the secondary winding causes current to flow in the secondary winding.

This current produces a flux field about the secondary shown as broken lines which is in opposition to the flux field about the primary Lenz's law. Thus, the flux about the secondary cancels some of the flux about the primary.