Electricity and Magnetism: electric circuits (internal resistance and series-parallel networks) – Week 1 focus
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Subject: Physical Sciences
Class: Grade 12
Term: 2nd Term
Week: 1
Theme: General lesson support
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This week, we delve into the fascinating world of electric circuits, focusing on the often-overlooked but critically important concepts of internal resistance and series-parallel networks. Understanding these principles is crucial, not just for excelling in Physical Sciences, but also for comprehending how electrical devices function in our daily lives. From the battery powering your phone during loadshedding to the complex electrical grid supplying electricity to our homes and businesses, internal resistance and network configurations play a significant role.
2.1 Internal Resistance (r): Every real battery or cell possesses internal resistance (represented by 'r'). This internal resistance arises from the materials within the battery hindering the flow of charge. Think of it as friction inside the battery. As current flows through the battery, some electrical energy is converted to heat due to this internal friction, reducing the voltage available to the external circuit. Imagine a group of learners trying to run a race. The battery is like the energy they have to run the race, and the internal resistance is like them running through mud. Some of their energy is used up just trying to get through the mud, leaving less energy for actually winning the race (powering the circuit). Electromotive Force (emf, ε): This is the total potential difference a battery can provide when no current is flowing. It's the battery's theoretical maximum voltage. Terminal Potential Difference (V terminal ): This is the actual voltage available across the terminals of the battery when current is flowing in the circuit. Because of the internal resistance, V terminal is always less than the emf (ε) when a current is flowing. The relationship between emf, terminal potential difference, current (I), and internal resistance is: V terminal = ε - Ir This equation tells us that the voltage available to the external circuit (V terminal ) is the battery's total voltage (ε) minus the voltage drop inside the battery due to the internal resistance (Ir). 2.2 Series Circuits: In a series circuit, components are connected one after another along a single path.
Total Resistance (R total ): The total resistance in a series circuit is the sum of the individual resistances: R total = R 1 + R 2 + R 3 + ...
Current (I): The current is the same at every point in a series circuit: I = I 1 = I 2 = I 3 = ...
Potential Difference (V): The total potential difference across a series circuit is the sum of the potential differences across each component: V = V 1 + V 2 + V 3 + ... 2.3 Parallel Circuits: In a parallel circuit, components are connected across each other, providing multiple paths for the current to flow.
Total Resistance (R total ): The reciprocal of the total resistance in a parallel circuit is the sum of the reciprocals of the individual resistances: 1/R total = 1/R 1 + 1/R 2 + 1/R 3 + ...
Therefore, R total = (1/(1/R 1 + 1/R 2 + 1/R 3 + ...))
Current (I): The total current entering a parallel circuit is the sum of the currents through each branch: I = I 1 + I 2 + I 3 + ...
Potential Difference (V): The potential difference is the same across each branch in a parallel circuit: V = V 1 = V 2 = V 3 = ... 2.4 Series-Parallel Networks: These circuits combine both series and parallel connections. To analyze them, we simplify the circuit step-by-step, calculating equivalent resistances for series and parallel sections until we have a simple series or parallel circuit that can be easily solved. 2.5 Cells in Series and Parallel: Series: Connecting cells in series increases the total emf. If n identical cells (each with emf ε and internal resistance r) are connected in series, the total emf is nε, and the total internal resistance is nr. Think of it like adding multiple batteries end-to-end to increase the voltage.
Parallel: Connecting cells in parallel increases the total current capacity but does not increase the emf. If n identical cells (each with emf ε and internal resistance r) are connected in parallel, the total emf remains ε, but the total internal resistance is r/n. This is like having multiple water pipes supplying water to the same point - the pressure (emf) stays the same, but the flow rate (current) increases. This configuration is often used in power banks to provide longer battery life at the same voltage.
Example 1: Internal Resistance
A battery with an emf of 12V and an internal resistance of 0.5Ω is connected to a resistor of 5.5Ω.
Calculate:
(a) The current in the circuit.
(b) The terminal potential difference of the battery.
Solution: