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# Transformers

## Characteristics of transformers

A transformer transfers electrical energy from one a.c. circuit to another a.c. circuit. They are used to switch between high and low voltages.

The two circuits involved do not touch and no current flows between them.

The transfer of energy involves an increase or decrease in voltage.

The primary coil is connected to the primary input voltage.

The secondary coil is connected to the secondary output voltage.

The alternating current running through the primary coil generates a changing magnetic field in the soft iron core.

This changing field induces an alternating e.m.f. in the secondary coil.

If the secondary coil is connected to a circuit, a secondary alternating current flows.

Transformers do not work with direct current! The current needs to change constantly to create the magnetic field required to induce an e.m.f.

## Step-up and step-down transformers

The ratio of the primary to the secondary voltages is related to the number of turns in the primary and secondary coils:

\begin{align*} \frac{\Tblue{\text{secondary voltage}}}{\Tred{\text{primary voltage}}} & = \frac{\Tblue{\text{number of turns in secondary coil}}}{\Tred{\text{number of turns in primary coil}}} \\ \frac{\Tblue{V_{\text{s}}}}{\Tred{V_{\text{p}}}} & = \frac{\Tblue{N_{\text{s}}}}{\Tred{N_{\text{p}}}} \end{align*}

Step-up transformers have more turns in the secondary coil than in the primary coil. This means that the output voltage is larger than the input voltage.

Step-down transformers have fewer turns in the secondary coil than in the primary coil. This means that the output voltage is smaller than the input voltage.

## Ideal transformers

Real transformers do not transfer all of the power in the primary coil to the secondary coil. Some of the power is lost as heat and other energy forms in the transformer.

An ideal transformer has no power loss. This means that the power in the primary coil $P_p$ is equal to the power in the secondary coil, $P_s$.

Ideal transformers do not exist! We consider ideal transformers to make the calculations simpler.

$$P_p = P_s$$

We can use the equation $\Tviolet{P}=\Tred{V}\Tblue{I}$ to link power, voltage and current.

$$\Tviolet{P_p} = \Tred{V_p} \Tblue{I_p} = \Tred{V_s} \Tblue{I_s}= \Tviolet{P_s}$$

This can be rearranged to

$$\frac{\Tred{V_p} }{\Tred{V_s}} = \frac{\Tblue{I_s}}{\Tblue{I_p}}$$

Since $\dfrac{V_p}{V_s}=\dfrac{N_p}{N_s}$, we can deduce that all three quantities are equal!

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

## Power loss in cables and transformers

Electric power is delivered from power stations to homes and offices in the form of alternating current.

A significant advantage of a.c. over d.c. for electricity distribution is that it is easier to change the voltage and current of a.c. using a transformer.

Electricity is transported at high voltages and low currents to limit power loss over long distances.

A transformer is then used to step-down (decrease) the voltage so that the electricity can be used in the home safely.

Electricity is transferred from power cables into homes.