Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

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Performance objectives

• Draw and interpret series-parallel circuit diagrams.
• Calculate the total resistance in series-parallel circuits.
• Explain the purpose and operation of different types of switches.
• Design a simple circuit with at least two switches.
• Troubleshoot a malfunctioning circuit.

Lesson summary

This week, we're diving deeper into electrical circuits, moving beyond simple series and parallel circuits to explore more complex circuits and the switches that control them. Understanding these concepts is crucial because electricity powers so much of our lives, from the lights in our homes and schools to the appliances we use every day. In South Africa, access to reliable electricity is vital for economic growth, education, and improving the quality of life for all citizens.

Lesson notes

Series-Parallel Circuits A series-parallel circuit is a combination of series and parallel connections. This means that some components are connected one after the other (series), while others are connected along multiple paths (parallel).

Analyzing Series-Parallel Circuits: To analyze these circuits, we need to simplify them step-by-step. This usually involves the following process: Identify Series and Parallel Sections: Carefully examine the circuit diagram to identify parts that are purely in series or purely in parallel. Calculate Equivalent Resistance for Parallel Sections: Use the formula for parallel resistance to find the equivalent resistance of each parallel section: 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 + ... Remember to take the reciprocal of the result to get R eq . Calculate Equivalent Resistance for Series Sections: Add the resistances of resistors in series: R eq = R 1 + R 2 + R 3 + ...

Repeat Steps 2 and 3: Continue simplifying the circuit by combining series and parallel sections until you have a single equivalent resistance representing the entire circuit.

Apply Ohm's Law: Use Ohm's Law (V = IR) to calculate the total current, voltage drops, and current through individual components.

Example 1: Consider a circuit with a 12V battery. Resistor R1 (10 Ohms) is in series with a parallel combination of R2 (20 Ohms) and R3 (30 Ohms). Calculate the total resistance and the total current in the circuit.

Solution: Parallel Section: R2 and R3 are in parallel. 1/R parallel = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 R parallel = 60/5 = 12 Ohms Series Section: R1 (10 Ohms) is in series with the equivalent parallel resistance (12 Ohms). R total = R1 + R parallel = 10 + 12 = 22 Ohms Total Current: Using Ohm's Law: I total = V / R total = 12V / 22 Ohms = 0.55 Amps (approximately) Therefore, the total resistance is 22 Ohms, and the total current flowing from the battery is approximately 0.55 Amps.

Example 2: Imagine a streetlight circuit. A 24V power supply connects to R1 (5 Ohms) in series with two parallel streetlights represented by R2 (15 Ohms) and R3 (15 Ohms). What is the current flowing through each streetlight?

Solution: Parallel Section: R2 and R3 are in parallel and have the same resistance. This makes the calculation simple. R parallel = R / N = 15 Ohms / 2 = 7.5 Ohms (where N is the number of identical resistors in parallel)

Series Section: R1 (5 Ohms) is in series with the equivalent parallel resistance (7.5 Ohms). R total = R1 + R parallel = 5 + 7.5 = 12.5 Ohms Total Current: Using Ohm's Law: I total = V / R total = 24V / 12.5 Ohms = 1.92 Amps Voltage across the parallel section: This can be calculated using Ohm’s law again, V = I * R V parallel = 1.92 Amps * 7.5 Ohms = 14.4 Volts Current through each streetlight: Since they are in parallel and have the same resistance, the current splits evenly. I streetlight = V parallel / R streetlight = 14.4V / 15 Ohms = 0.96 Amps Therefore, the current flowing through each streetlight is 0.96 Amps. Switches Switches are essential components that control the flow of electricity in a circuit. They act as gatekeepers, allowing or blocking current to different parts of the circuit. Different types of switches offer different functionalities: SPST (Single-Pole Single-Throw): This is the simplest type of switch. It has one input terminal (pole) and one output terminal (throw). It either opens (off) or closes (on) the circuit. Think of a simple light switch in your room.

SPDT (Single-Pole Double-Throw): This switch has one input terminal (pole) and two output terminals (throws). It can connect the input to either of the two outputs, but not both at the same time. Consider a switch that selects which speaker plays music.

DPST (Double-Pole Single-Throw): This switch has two input terminals (poles) and two output terminals (throws). It acts like two SPST switches that are controlled together. It can simultaneously open or close two separate circuits. Often used for safety reasons to isolate both the live and neutral wires in an appliance.

DPDT (Double-Pole Double-Throw): This switch has two input terminals (poles) and four output terminals (throws). Each input can be connected to either of its two corresponding outputs. This offers complex control and can be used for things like reversing the polarity of a motor.

Example of Switch Application: Imagine you want to build a simple circuit that controls two LEDs (Light Emitting Diodes) with one switch. You want one LED to be on when the switch is in one position, and the other LED to be on when the switch is in the other position. You would use an SPDT switch. The common terminal of the SPDT switch connects to the positive terminal of the battery. Each of the other two terminals connects to one LED and a resistor. The other end of the LED and resistor connects to the negative terminal of the battery.