Lesson Notes By Weeks and Term v5 - Grade 10

Lesson Video

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Performance objectives

• Calculate total resistance in series & parallel circuits.
• Determine current through each component.
• Calculate voltage drop across each component.
• Analyse power dissipated in circuits.
• Compare characteristics of series vs. parallel circuits.

Lesson summary

This week, we delve into the fascinating world of Direct Current (DC) circuits. Understanding DC circuits, specifically series and parallel configurations, is fundamental to comprehending how many electrical devices we use daily function. From the cellphones we use to connect with family across the country, to the lighting systems in our homes and schools powered by inverters during load shedding, the principles of series and parallel circuits are at play. Moreover, with the growing importance of renewable energy sources like solar power in South Africa, understanding DC circuits is crucial for designing and maintaining solar panel installations.

Lesson notes

2.1 What is a DC Circuit? A DC (Direct Current) circuit is a closed loop that allows current to flow in only one direction. This is unlike AC (Alternating Current) circuits, where the current direction changes periodically. In DC circuits, a voltage source (like a battery or a solar panel) provides the electrical energy that drives the current through the circuit components (resistors, lamps, etc.). 2.2 Series Circuits In a series circuit, all components are connected one after the other along a single path. This means the same current flows through every component. Think of it like a single lane road; all cars must travel the same road.

Total Resistance (R T ): The total resistance in a series circuit is the sum of the individual resistances. R T = R 1 + R 2 + R 3 + ...

Current (I): The current is the same at all points in the series circuit.

It can be calculated using Ohm's Law: I = V T / R T where V T is the total voltage.

Voltage Drop (V): The voltage drop across each resistor is proportional to its resistance.

You can calculate it using Ohm's Law: V 1 = I R 1 , V 2 = I R 2 , V 3 = I * R 3 , ... The sum of the voltage drops across all resistors equals the total voltage supplied (Kirchhoff's Voltage Law): V T = V 1 + V 2 + V 3 + ...

Power (P): The power dissipated by each resistor is given by: P 1 = I 2 R 1 or P 1 = V 1 I The total power dissipated in the circuit is: P T = I 2 R T or P T = V T I The sum of individual power dissipations equals the total power dissipation.

Example 1: Series Circuit Consider a series circuit with a 12V battery connected to three resistors: R 1 = 10Ω, R 2 = 20Ω, and R 3 = 30Ω.

Calculate the total resistance: R T = 10Ω + 20Ω + 30Ω = 60Ω Calculate the current: I = V T / R T = 12V / 60Ω = 0.2A Calculate the voltage drop across each resistor: V 1 = I R 1 = 0.2A 10Ω = 2V V 2 = I R 2 = 0.2A 20Ω = 4V V 3 = I R 3 = 0.2A 30Ω = 6V (Check: 2V + 4V + 6V = 12V = V T ) Calculate the power dissipated by each resistor and the total power: P 1 = I 2 R 1 = (0.2A) 2 10Ω = 0.4W P 2 = I 2 R 2 = (0.2A) 2 20Ω = 0.8W P 3 = I 2 R 3 = (0.2A) 2 30Ω = 1.2W P T = I 2 R T = (0.2A) 2 60Ω = 2.4W (Check: 0.4W + 0.8W + 1.2W = 2.4W = P T ) 2.3 Parallel Circuits In a parallel circuit, components are connected across each other, providing multiple paths for the current to flow. This means the same voltage is applied across every component. Imagine multiple lanes on a highway splitting; cars can choose different paths, but all start and end at the same points.

Total Resistance (R T ): 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 + ... R T = 1 / (1/R 1 + 1/R 2 + 1/R 3 + ...) For only two resistors in parallel, a simplified formula can be used: R T = (R 1 * R 2 ) / (R 1 + R 2 )

Voltage (V): The voltage is the same across all branches in a parallel circuit. V 1 = V 2 = V 3 = V T Current (I): The total current is the sum of the currents through each branch (Kirchhoff's Current Law): I T = I 1 + I 2 + I 3 + ... The current through each branch can be calculated using Ohm's Law: I 1 = V T / R 1 , I 2 = V T / R 2 , I 3 = V T / R 3 , ...

Power (P): The power dissipated by each resistor is given by: P 1 = V T 2 / R 1 or P 1 = V T * I 1 The total power dissipated in the circuit is: P T = V T 2 / R T or P T = V T * I T The sum of individual power dissipations equals the total power dissipation.

Example 2: Parallel Circuit Consider a parallel circuit with a 6V battery connected to two resistors: R 1 = 12Ω and R 2 = 6Ω.

Calculate the total resistance: R T = (12Ω * 6Ω) / (12Ω + 6Ω) = 72Ω / 18Ω = 4Ω Calculate the current through each resistor: I 1 = V T / R 1 = 6V / 12Ω = 0.5A I 2 = V T / R 2 = 6V / 6Ω = 1A Calculate the total current: I T = I 1 + I 2 = 0.5A + 1A = 1.5A Calculate the power dissipated by each resistor and the total power: P 1 = V T 2 / R 1 = (6V) 2 / 12Ω = 36V 2 / 12Ω = 3W P 2 = V T 2 / R 2 = (6V) 2 / 6Ω = 36V 2 / 6Ω = 6W P T = V T 2 / R T = (6V) 2 / 4Ω = 36V 2 / 4Ω = 9W (Check: 3W + 6W = 9W = P T ) 2.4 Series-Parallel Circuits Many real-world circuits are a combination of series and parallel arrangements. To analyse these circuits, we simplify them step-by-step. First, identify sections that are purely series or purely parallel and calculate their equivalent resistance. Then, replace that section with its equivalent resistance and repeat the process until you have a simple series or parallel circuit.

Example 3: Series-Parallel Circuit Consider a circuit with a 24V battery. Resistor R 1 = 4Ω is in series with a parallel combination of R 2 = 12Ω and R 3 = 6Ω. Calculate the equivalent resistance of the parallel section (R 2 and R 3 ): R P = (12Ω * 6Ω) / (12Ω + 6Ω) = 72Ω / 18Ω = 4Ω Replace the parallel combination with its equivalent resistance (R P = 4Ω). Now, R 1 and R P are in series.