Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Explain the operating principle of a transformer.
• Calculate voltage, current, and turns ratios.
• Calculate transformer efficiency and identify power losses.
• Describe the components of a power distribution system.
• Explain the purpose of high-voltage transmission.

Lesson summary

This week, we delve into the crucial world of transformers and power distribution. Understanding these concepts is vital for every South African. From the electricity powering our homes and schools to the functioning of industries and businesses, efficient power distribution, facilitated by transformers, is fundamental. Load shedding, a persistent challenge in South Africa, underscores the importance of optimizing our power distribution networks. Understanding how transformers work and how power is distributed allows us to better understand these challenges and potentially contribute to solutions.

Lesson notes

2.1 The Transformer: Principles of Operation A transformer is a static device that transfers electrical energy from one circuit to another through electromagnetic induction. It consists of two or more coils of wire electrically isolated but magnetically linked through a common ferromagnetic core. The core is typically laminated to reduce eddy current losses.

Electromagnetic Induction: The principle underlying transformer operation is electromagnetic induction, discovered by Faraday. When an alternating current flows through the primary coil (also called the input winding), it creates a changing magnetic flux in the core. This changing flux induces an electromotive force (EMF) or voltage in the secondary coil (also called the output winding).

Faraday's Law: Faraday's Law of Electromagnetic Induction states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux through the coil. Mathematically, EMF = -N(dΦ/dt), where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux.

Turns Ratio: The ratio of the number of turns in the primary coil (N p ) to the number of turns in the secondary coil (N s ) is called the turns ratio (a): a = N p /N s . This ratio determines the voltage transformation. 2.2 Transformer Voltage and Current Relationships Voltage Ratio: The voltage ratio is directly proportional to the turns ratio: V p /V s = N p /N s = a, where V p is the primary voltage and V s is the secondary voltage.

Current Ratio: The current ratio is inversely proportional to the turns ratio: I p /I s = N s /N p = 1/a, where I p is the primary current and I s is the secondary current. This relationship assumes an ideal transformer (no losses).

Step-Up and Step-Down Transformers: Step-Up Transformer: If N s > N p (a s p (a > 1), the secondary voltage is lower than the primary voltage, and the transformer is called a step-down transformer. This is used to reduce the voltage to usable levels for homes and businesses.

Example 1: A transformer has a primary winding with 500 turns and a secondary winding with 100 turns. If the primary voltage is 220 V, calculate the secondary voltage.

Solution: Turns ratio (a) = N p /N s = 500/100 = 5 V p /V s = a 220/V s = 5 V s = 220/5 = 44

V. This is a step-down transformer.

Example 2: A transformer connected to a 220V supply has a turns ratio of 1:

1

0. Calculate the secondary voltage.

Solution: N p /N s = 1/10 = 0.1 V p /V s = N p /N s 220/V s = 0.1 V s = 220/0.1 = 2200

V. This is a step-up transformer.

Example 3: A transformer has a primary current of 5A and a secondary current of 25A. If the secondary winding has 100 turns, determine the number of turns in the primary winding.

Solution: I p /I s = N s /N p 5/25 = 100/N p N p = (100 25)/5 = 500 turns 2.3 Transformer Efficiency and Power Losses No transformer is perfectly efficient. Some energy is always lost in the form of heat. Transformer efficiency (η) is defined as the ratio of output power (P out ) to input power (P in ): η = (P out /P in ) 100% P in = V p I p * cos(θ) where cos(θ) is the power factor. P out = V s I s * cos(θ) The main causes of power losses in transformers are: Copper Losses (I 2 R Losses): These losses occur due to the resistance of the copper windings. The power dissipated as heat is proportional to the square of the current flowing through the windings and the resistance of the windings (P = I 2 R). To minimize these losses, thick copper conductors are used.

Iron Losses (Core Losses): These losses occur in the transformer core and are of two types: Hysteresis Losses: These losses are due to the energy required to repeatedly magnetize and demagnetize the core material during each AC cycle. Using core materials with a narrow hysteresis loop minimizes this.

Eddy Current Losses: These losses are due to circulating currents induced in the core by the changing magnetic flux. Laminating the core reduces the path for these currents, increasing the resistance and therefore reducing the magnitude of the eddy currents.

Example 4: A transformer takes 1000W of power and delivers 950W to the load. Calculate the efficiency of the transformer.

Solution: η = (P out /P in ) 100% η = (950/1000) 100% = 95% 2.4 Power Distribution System Components A power distribution system is a network that carries electricity from generation sources to individual consumers.

The key components include: Power Plants/Generation Stations: Where electricity is generated (e.g., coal-fired power plants like Medupi and Kusile, hydro-electric plants, solar farms).

Transmission Lines: High-voltage lines that carry electricity over long distances from generation plants to substations. These lines are designed to minimize losses over long distances.

Substations: Facilities that step down the voltage from high transmission levels to lower distribution levels. Substations also contain switchgear, protective devices, and control equipment.