# 7.10.4 The Operation of a Transformer

### The Transformer Equation

• A transformers is

A device which changes high alternating voltage at low current to low alternating voltage at high current, and vice versa

• This is to reduce heat energy lost whilst electricity is transmitted down electrical power lines from power stations to the national grid
• A transformer is made up of:
• A primary coil
• A secondary coil
• Laminated soft iron core
• The primary and secondary coils are wound around the laminated soft iron core
• The soft iron core is necessary to strengthen the magnetic field and reduces eddy currents induced in the iron core
• At the primary coil, alternating current produces an alternating voltage is applied
• This sets up a changing magnetic field inside the iron core and therefore a changing magnetic flux linkage
• A changing magnetic field also passes through to the secondary coil
• This results in a changing magnetic flux linkage in the secondary coil and from Faraday’s Law, an e.m.f is induced
• This produces an alternating output voltage from the wire wrapped around the secondary coil
• The transformer equation is defined as: • Where:
• Vp = voltage in the primary coil (V)
• Vs = output voltage from the secondary coil (V)
• Np = number of turns in the primary coil
• Ns = number of turns in the secondary coil
• For an ideal transformer, there is no electrical energy lost and it is 100% efficient
• This means the power in the primary coil equals the power in the second coil

VpIp = VsIs

• Where:
• Ip = current in the primary coil (A)
• Is = output current from the secondary coil (A)
• This means the ideal transformer equation can be written as: • The two types of transformers are:
• Step-up transformer (increases the voltage of the power source) where Ns > Np
• Step-down transformer (decreases the voltage of the power source) where Np > Ns

#### Worked Example

A step-down transformer turns a primary voltage of 0.5 kV into a secondary voltage of 100 V.

Calculate the number of turns needed in the secondary coil if the primary coil contains 3000 turns of wire.

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