Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Define electromagnetic induction and its role in transformers.
• Describe the construction of a basic transformer.
• Explain voltage and current relationships using the turns ratio.
• Calculate key transformer parameters.
• Identify different types of transformer cores.

Lesson summary

This week, we're diving into the heart of electrical power systems: transformers and power distribution. Transformers are the unsung heroes of electricity. Without them, we wouldn't be able to efficiently transmit power over long distances from power stations (like Medupi or Koeberg) to our homes, schools, and businesses. Understanding transformers is crucial for anyone interested in electrical technology, as they play a vital role in ensuring a stable and reliable power supply. In South Africa, with its vast distances and growing energy demands, efficient power distribution is essential for economic growth and improving the quality of life for all citizens.

Lesson notes

2.1 Electromagnetic Induction The fundamental principle behind the operation of a transformer is electromagnetic induction. This is the process where a changing magnetic field induces a voltage in a conductor. Michael Faraday discovered this principle. Imagine a coil of wire (the secondary winding) placed near another coil of wire (the primary winding). If we apply an alternating current (AC) to the primary winding, it creates a constantly changing magnetic field. This changing magnetic field cuts through the secondary winding, inducing a voltage in it. Crucially, it's the changing magnetic field that's important – a steady magnetic field will not induce a voltage. The magnitude of the induced voltage is directly proportional to the rate of change of the magnetic flux (the magnetic field lines passing through the coil) and the number of turns in the coil. This relationship is formalized in Faraday's Law of Induction: `E = -N(dΦ/dt)` Where: `E` is the induced voltage (in Volts) `N` is the number of turns in the coil `dΦ/dt` is the rate of change of magnetic flux (in Webers per second) The negative sign indicates that the induced voltage opposes the change in magnetic flux, as per Lenz's Law. 2.2 Transformer Construction A basic transformer consists of the following key components: Core: The core provides a path for the magnetic flux. It's typically made of laminated silicon steel. Lamination is crucial to minimize eddy current losses. Eddy currents are circulating currents induced in the core material by the changing magnetic field. These currents generate heat, wasting energy. Lamination reduces the magnitude of these currents by breaking the core into thin, insulated sheets.

Common core types include: Core-type: Windings surround the core.

Shell-type: Core surrounds the windings. Shell-type transformers generally offer better magnetic coupling.

Toroidal-type: Core is shaped like a ring, providing even better magnetic coupling and reduced leakage flux.

Primary Winding: This is the winding connected to the input AC voltage source. It carries the current that creates the changing magnetic field. We denote the number of turns in the primary winding as `N_p` and the voltage as `V_p`.

Secondary Winding: This is the winding where the induced voltage appears. It is connected to the load. We denote the number of turns in the secondary winding as `N_s` and the voltage as `V_s`. 2.3 Transformer Equations: Turns Ratio, Voltage Ratio, and Current Ratio The relationship between the number of turns in the primary and secondary windings determines the voltage and current transformation.

The turns ratio (a) is defined as: `a = N_p / N_s` For an ideal transformer (no losses), the voltage ratio is directly proportional to the turns ratio: `V_p / V_s = a` or `V_s = V_p / a` Therefore, if `a > 1`, the transformer is a step-down transformer (the secondary voltage is lower than the primary voltage). If `a < 1`, the transformer is a step-up transformer (the secondary voltage is higher than the primary voltage). In an ideal transformer, power is conserved.

Therefore, the input power is equal to the output power: `P_p = P_s` or `V_p I_p = V_s I_s` Where: `I_p` is the primary current `I_s` is the secondary current Therefore, the current ratio is inversely proportional to the turns ratio: `I_p / I_s = V_s / V_p = 1/a` or `I_s = a * I_p` This means that in a step-down transformer, the current in the secondary winding is higher than the current in the primary winding, and vice-versa for a step-up transformer.

Important Considerations: These equations are based on the ideal transformer model, which assumes no losses. In reality, transformers have losses due to factors like winding resistance, core hysteresis, and eddy currents.

However, these equations provide a good approximation for understanding the fundamental principles. 2.4 Worked Examples Example 1: Step-Down Transformer A transformer connected to a 220V AC supply has a primary winding with 1000 turns. The secondary winding has 100 turns. What is the secondary voltage?

Solution: `V_p = 220V` `N_p = 1000` `N_s = 100` `a = N_p / N_s = 1000 / 100 = 10` `V_s = V_p / a = 220V / 10 = 22V` Therefore, the secondary voltage is 22

V. This is a step-down transformer.

Example 2: Step-Up Transformer A transformer has a turns ratio of 0.

1. If the primary voltage is 12V, what is the secondary voltage? If the primary current is 5A, what is the secondary current (assuming an ideal transformer)?

Solution: `a = 0.1` `V_p = 12V` `I_p = 5A` `V_s = V_p / a = 12V / 0.1 = 120V` `I_s = a I_p = 0.1 * 5A = 0.5A` Therefore, the secondary voltage is 120V and the secondary current is 0.5

A. This is a step-up transformer.

Example 3: Determining Turns Ratio A transformer is required to step down a voltage from 11kV (typical distribution voltage) to 220V for domestic use. What turns ratio is required?