Lesson Notes By Weeks and Term v5 - Grade 12

Lesson Video

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Performance objectives

• Identify and describe resistors, capacitors, and inductors.
• Calculate total resistance in series and parallel circuits.
• Explain the function and time constant of capacitors.
• Describe the principles of inductors and inductive reactance.
• Construct and test basic series and parallel circuits.

Lesson summary

This week, we delve deeper into fundamental electronic components and how they combine to create basic circuits. Understanding these building blocks is crucial because electronic devices are integral to modern life in South Africa, from cell phones and computers to renewable energy systems like solar panels and traffic lights. A solid understanding of electronics opens doors to careers in telecommunications, renewable energy, manufacturing, and many other rapidly growing fields within our country.

Lesson notes

2.1 Resistors Resistors are passive components that oppose the flow of electric current. Their resistance is measured in Ohms (Ω). A resistor's value is often indicated by color bands (the resistor color code). Tolerance indicates the accuracy of the resistor's stated value. Power rating indicates the maximum power a resistor can dissipate without being damaged.

Ohm's Law: A fundamental relationship in circuit analysis: V = IR, where V is voltage (in Volts), I is current (in Amperes), and R is resistance (in Ohms). This law shows the direct proportionality between voltage and current for a given resistance.

Resistor Color Code: Understanding the resistor color code is essential for quickly determining a resistor's value. The standard code uses coloured bands to represent digits, multipliers, and tolerance.

A typical resistor has four bands: the first two represent the first two digits of the resistance value, the third represents the multiplier (power of 10), and the fourth represents the tolerance. 5-band resistors exist for more precise values.

Series Resistors: When resistors are connected in series, the total resistance (R T ) is the sum of the individual resistances: R T = R 1 + R 2 + R 3 + ... The same current flows through each resistor in a series circuit.

Parallel Resistors: When resistors are connected in parallel, the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances: 1/R T = 1/R 1 + 1/R 2 + 1/R 3 + ... The voltage across each resistor in a parallel circuit is the same.

Example 1: Resistor Color Code A resistor has the following color bands: Brown, Black, Red, Gold. Brown = 1 Black = 0 Red = x10 2 (or 100) Gold = ±5% tolerance Therefore, the resistor value is 10 x 100 = 1000 Ω or 1 kΩ, with a 5% tolerance. This means the actual resistance could be between 950 Ω and 1050 Ω.

Example 2: Series Resistors Three resistors are connected in series: R 1 = 100 Ω, R 2 = 220 Ω, and R 3 = 330 Ω. Calculate the total resistance. R T = R 1 + R 2 + R 3 = 100 Ω + 220 Ω + 330 Ω = 650 Ω Example 3: Parallel Resistors Two resistors are connected in parallel: R 1 = 1 kΩ and R 2 = 2 kΩ. Calculate the total resistance. 1/R T = 1/R 1 + 1/R 2 = 1/1000 + 1/2000 = 0.001 + 0.0005 = 0.0015 R T = 1/0.0015 = 666.67 Ω (approximately) 2.2 Capacitors Capacitors are passive components that store electrical energy in an electric field. They consist of two conductive plates separated by an insulating material called a dielectric. Capacitance is measured in Farads (F), but commonly encountered values are in microfarads (µF), nanofarads (nF), and picofarads (pF).

Capacitance Formula: Q = CV, where Q is the charge stored (in Coulombs), C is the capacitance (in Farads), and V is the voltage across the capacitor (in Volts).

Charging and Discharging: When a voltage is applied to a capacitor, it charges up, storing energy. When the voltage source is removed, the capacitor discharges, releasing the stored energy. RC Time Constant (τ): In a circuit containing a resistor and a capacitor (RC circuit), the time constant (τ) is the time it takes for the capacitor to charge or discharge to approximately 63.2% of its final value. τ = RC, where R is the resistance in Ohms and C is the capacitance in Farads. After 5 time constants (5τ), the capacitor is considered fully charged (or discharged). 2.3 Inductors Inductors are passive components that store electrical energy in a magnetic field. They consist of a coil of wire. Inductance is measured in Henrys (H), but commonly encountered values are in millihenrys (mH) and microhenrys (µH).

Inductance: The property of an inductor to oppose changes in current. The inductance (L) of a coil depends on its geometry (number of turns, coil diameter, and core material).

Inductive Reactance (X L ): The opposition to the flow of alternating current (AC) offered by an inductor. X L = 2πfL, where f is the frequency of the AC signal in Hertz (Hz) and L is the inductance in Henrys (H). Inductive reactance increases with increasing frequency. Inductors essentially block high-frequency signals while allowing low-frequency signals to pass.

Example 4: RC Time Constant A circuit contains a 10 kΩ resistor and a 100 µF capacitor connected in series. Calculate the time constant. τ = RC = (10,000 Ω) x (100 x 10 -6 F) = 1 second. This means it takes 1 second for the capacitor to charge to 63.2% of its maximum voltage or discharge to 36.8% of its initial voltage.

Example 5: Inductive Reactance An inductor has an inductance of 10 mH. Calculate its inductive reactance at a frequency of 50 Hz (South African mains frequency). X L = 2πfL = 2π x 50 Hz x 0.01 H = 3.14 Ω (approximately) Guided Practice (With Solutions)

Question 1: A resistor has the following color code: Red, Red, Brown, Gold. What is its resistance and tolerance?

Solution: Red = 2 Red = 2 Brown = x10 1 (or 10) Gold = ±5% Resistance = 22 x 10 = 220 Ω, with a tolerance of ±5%.