6.6.6 Transformers

• A transformer is defined as:

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

• This is designed to reduce heat energy lost whilst electricity is transmitted down electrical power lines from power stations to the national grid
  • It increases the efficiency of electrical transmission
  • This is because the power dissipated by a resistor is given by P = I²R
  • Therefore, reducing the current also reduces the power loss through the transmission cables
• Transformers are therefore used in the National Grid to increase efficiency of transmission.
  • Electrical power cables have a high voltage and low current due to the use of step-up transformers
  • A step-down transformer is used at a substation near people's homes and businesses to reduce the voltage and increase the current

Electricity is transmitted at high voltage, reducing the current and hence power loss in the cables using transformers

• A transformer is made up of:
  • A primary coil
  • A secondary coil
  • A soft iron core

• The primary and secondary coils are wound around the soft iron core
  • The soft iron core is necessary because it focuses and directs the magnetic field from the primary to the secondary coil
  • Soft iron is used because it can easily be magnetised and demagnetised

A step-up transformer has more turns in the secondary coil than primary

• In the primary coil, an alternating current producing an alternating voltage is applied
  • This creates an alternating magnetic field inside the iron core and therefore a changing magnetic flux linkage

• A changing magnetic field passes through to the secondary coil through the iron core
  • This results in a changing magnetic flux linkage in the secondary coil
  • Hence, from Faraday's Law, an e.m.f. is induced

• An e.m.f. produces an alternating output voltage from the secondary coil
  • The output alternating voltage is at the same frequency as the input voltage
• The magnitude of the e.m.f. is determined by the number of coils
  • A step-up transformer has more coils in the secondary than the primary and the secondary voltage is larger than the primary voltage
  • A step-down transformer has more coils in the primary than the secondary and the secondary voltage is smaller than the primary voltage

Transformer Calculations

• The transformer equation is:

• Where:
  • N_s = number of turns in the secondary coil
  • N_p = number of turns in the primary coil
  • _Vs = output voltage from the secondary coil (V)
  • _Vp = input voltage in the primary coil (V)

• There are two types of transformers:
  • Step-up transformer (increases the voltage of the power source) where N_s > N_p
  • Step-down transformer (decreases the voltage of the power source) where N_p > N_s

• 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;

• Where:
• • I_p = current in the primary coil (A)
  • I_s = output current from the secondary coil (A)

Step 1: List the known quantities

• • Primary voltage, V_p = 0.5 kV = 0.5 × 10³ V
  • Secondary voltage, V_s = 100 V
  • Number of turns in the primary coil, N_p = 3000 turns

Step 2: Write down the transformer equation

Step 3: Rearrange for number of turns in the secondary coil

Step 4: Substitute in the values

turns

• A simple investigation can be conducted to investigate the transformer equations

Equipment

• Iron rod
• Two 1m lengths of insulated copper wire
• A.c. power supply
• 2 multimeters set to measure a.c. voltage
• 2 multimeters set to measure a.c. current
• Crocodile clips and leads

Method

1. Wind 20 loops of copper wire around the iron rod at one end
   • Wind 10 loops around the other end, using the other piece of wire
2. Connect the first loop to the power pack using the leads and crocodile clips
   • Include a multimeter to measure a.c. voltage across the wire and a multimeter to measure a.c. current in the wire
3. Connect the multimeters to measure a.c. current and voltage to the second wire.
4. Turn on the power pack
   • Record the values of voltage and current in each coil in a suitable table
5. Keeping 20 turns in the initial coil, vary the number of coils in the output coil
   • Record the values of current and voltage for each

Analysis

• For an ideal transformer:

• Using the values recorded for V_p, N_p and N_s, calculate the expected value of V_s for each value
  • Compare with the record value
• Do similar with the current
• Plotting a graph of N_s against V_s should give a straight line graph as V_s increases in proportion with number of turns

Evaluation

•   The iron core may heat up
  • This is due to the formation of eddy currents in the core
  • Transformers are often laminated
  • This is where layers of iron are glued together, rather than a single block of iron being used
• Some energy will be lost due to the resistance of the wire
  • Using insulated wire minimises heating due to resistance