Lesson Notes By Weeks and Term v3 - Senior Secondary 1
Relationships between current, voltage and resistant
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Relationships between current, voltage and resistant
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Subject: Basic Electronics
Class: Senior Secondary 1
Term: 2nd Term
Week: 1
Theme: Electrical Quantities
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Explain the following quantities: voltage, current and resistance. State the units, symbols and in struments for measuring the quantities mentioned in (1) above. State Ohm’s Law. Perform a simple experiment to determine Ohm’s Law. Calculate current, voltage and resistance in a given circuit.
when a potential difference of one Volt is applied across it.
Multiples: kilo-ohm (kΩ, 103 Ω), mega-ohm (MΩ, 106 Ω).
Measuring Instrument: Resistance can be measured directly using an Ohmmeter when the component is disconnected from any power source. In a live circuit, it is calculated using Ohm's Law (R = V/I).
D. Ohm's Law Statement: Ohm's Law states that the current flowing through a metallic conductor is directly proportional to the potential difference (voltage) across its ends, provided that the physical conditions (especially temperature) remain constant.
Formula: Mathematically, this relationship is expressed as: $V \propto I$ (at constant temperature)
Which leads to the equation: V = I × R Where: V = Voltage (in Volts, V) I = Current (in Amperes, A) R = Resistance (in Ohms, Ω)
Derived Formulas: Ohm's Law can be rearranged to find any of the three quantities if the other two are known: To find Current: I = V / R To find Resistance: R = V / I Ohm's Law Triangle: A common mnemonic tool to remember the formulas: ``` V --- I | R ``` To find a quantity, cover it up: Cover V: I × R Cover I: V / R Cover R: V / I Ohmic vs.
Non-Ohmic Conductors: Ohmic Conductors: Materials that obey Ohm's Law (i.e., their resistance remains constant regardless of the applied voltage or current). A plot of V vs. I for an ohmic conductor is a straight line passing through the origin.
Examples: most metallic conductors like copper wire, standard resistors.
Non-Ohmic Conductors: Materials that do not obey Ohm's Law. Their resistance changes with voltage or current. A plot of V vs. I is not a straight line.
Examples: diodes, transistors, thermistors, filament lamps (due to temperature change). Worked Examples (Relevant to Nigerian Contexts): Example 1: Calculating Voltage A rechargeable standing fan used in a Nigerian home during a power outage has a motor with a resistance of 24 Ω. If a current of 0.5 A flows through the motor, what is the voltage supplied to the motor?
Given: Resistance (R) = 24 Ω Current (I) = 0.5 A Formula: V = I × R Calculation: V = 0.5 A × 24 Ω V = 12 V Answer: The voltage supplied to the fan motor is 12 Volts. This might represent the voltage of the fan's internal battery.
Example 2: Calculating Current A local electrician is testing a heating element for an electric kettle. The element is designed to operate on a 230 V (NEPA supply) and has a resistance of 50 Ω. What is the current that will flow through the heating element?
Given: Voltage (V) = 230 V Resistance (R) = 50 Ω Formula: I = V / R Calculation: I = 230 V / 50 Ω I = 4.6 A Answer: A current of 4.6 Amperes will flow through the heating element. This current value is important for selecting the correct fuse for the kettle.
Example 3: Calculating Resistance A security light in a compound powered by a small solar inverter draws a current of 0.2 A when connected to a 12 V battery. What is the resistance of the light bulb?
Given: Voltage (V) = 12 V Current (I) = 0.2 A Formula: R = V / I Calculation: R = 12 V / 0.2 A R = 60 Ω * Answer: The resistance of the security light bulb is 60 Ohms. --- This section provides in-depth explanations of the core concepts.
A. Electric Current (I)
Definition: Electric current is defined as the rate of flow of electric charge (electrons) through a conductor. In simpler terms, it is the movement of free electrons from one point to another in a circuit.
Analogy: Imagine water flowing through a pipe. The amount of water passing a certain point per second is analogous to electric current.
Direction of Flow: Conventional Current: Flows from the positive terminal to the negative terminal of a power source. This is the historical direction, still widely used in circuit analysis.
Electron Flow: Flows from the negative terminal to the positive terminal (since electrons are negatively charged and are attracted to the positive terminal).
Symbol: The standard symbol for current is
I. Unit: The SI unit of current is the Ampere (A). One Ampere is defined as one Coulomb of charge passing a point in one second (1 A = 1 C/s).
Sub-multiples: milliampere (mA, 10−3 A), microampere (μA, 10−6 A).
Measuring Instrument: Current is measured using an Ammeter.
Connection in Circuit: An ammeter must always be connected in series with the component or part of the circuit where the current is to be measured. This ensures that the entire current flows through the ammeter. An ideal ammeter has very low (ideally zero) resistance.
B. Voltage / Potential Difference (V)
Definition: Voltage, also known as potential difference or electromotive force (EMF) when referring to a source, is the energy required to move a unit charge between two points in an electric field. It is the "push" or "force" that drives the electric current.
Analogy: Using the water pipe analogy, voltage is similar to the water pressure difference between two points in the pipe, which causes the water to flow. A higher pressure difference results in a stronger flow.
Symbol: The standard symbol for voltage is V (or E for EMF).
Unit: The SI unit of voltage is the Volt (V). One Volt is defined as one Joule of energy per Coulomb of charge (1 V = 1 J/C).
Multiples: kilovolt (kV, 103 V).
Measuring Instrument: Voltage is measured using a Voltmeter.
Connection in Circuit: A voltmeter must always be connected in parallel across the two points where the potential difference is to be measured. This ensures that it measures the voltage across those points. An ideal voltmeter has very high (ideally infinite) resistance.
C. Resistance (R)
Definition: Resistance is the opposition to the flow of electric current in a conductor. All materials offer some resistance to current flow, with conductors having low resistance and insulators having very high resistance.
Analogy: In the water pipe analogy, resistance is like the friction or narrowness of the pipe that restricts water flow. A narrower pipe or rougher inner surface offers more resistance to water flow.
Factors Affecting Resistance:
1. Length (L): Resistance is directly proportional to the length of the conductor (longer wire = more resistance).
2. Cross-sectional Area (A): Resistance is inversely proportional to the cross-sectional area of the conductor (thicker wire = less resistance).
3. Material (ρ - resistivity): Resistance depends on the type of material. Some materials conduct better than others (e.g., copper has lower resistivity than iron).
4. Temperature: For most conductors, resistance increases with temperature.
Symbol: The standard symbol for resistance is
R. Unit: The SI unit of resistance is the Ohm (Ω). One Ohm is defined as the resistance that allows one Ampere of current to flow when a potential difference of one Volt is applied across it.
Multiples: kilo-ohm (kΩ, 103 Ω), mega-ohm (MΩ, 106 Ω).
Measuring Instrument: Resistance can be measured directly using an Ohmmeter when the component is disconnected from any power source. In a live circuit, it is calculated using Ohm's Law (R = V/I).
D. Ohm's Law Statement: Ohm's Law states that the current flowing through a metallic conductor is directly proportional to the potential difference (voltage) across its ends, provided that the physical conditions (especially temperature) remain constant.
Formula: This section outlines practical activities for both the teacher and students.
Teacher Activities:
1. Introduction and Engagement: Begin by asking students about their experiences with electricity (e.g., power outages, use of generators, charging phones, electric appliances). Introduce the concept of electricity as the flow of 'something' and pose questions like "What makes it flow?", "What slows it down?".
Introduce the water pipe analogy: Water flow = Current Water pressure = Voltage Pipe diameter/friction = Resistance Relate these to everyday Nigerian scenarios: "Why does a big generator power more things than a small one (voltage/current capacity)?" "Why do some phone chargers charge faster (current delivery)?"
2. Concept Explanation (A, B, C): Current: Explain charge flow, unit (Ampere), symbol (I). Demonstrate an ammeter (physical device or clear picture/video) and emphasize its series connection. Show a simple circuit diagram.
Voltage: Explain potential difference, "electrical push," unit (Volt), symbol (V). Demonstrate a voltmeter (physical device or clear picture/video) and emphasize its parallel connection. Show a simple circuit diagram.
Resistance: Explain opposition to flow, unit (Ohm), symbol (R). Discuss factors affecting resistance (length, area, material, temperature) using examples like thin vs. thick wires, copper vs. iron wires. Demonstrate an ohmmeter (if available).
3. Ohm's Law Explanation (D): Introduce Ohm's Law as the fundamental relationship between V, I, and
R. State the law clearly: "Current is directly proportional to voltage and inversely proportional to resistance." Derive the formula V = IR and its variations (I = V/R, R = V/I). Draw the Ohm's Law triangle as a mnemonic. Work through the provided "Worked Examples" demonstrating step-by-step calculations and clearly explaining each step. Ensure these examples resonate with local scenarios.
4. Ohm's Law Experiment Demonstration/Guidance: Setup: The teacher should have the following components prepared: a DC power supply (e.g., 2-3 x 1.5V D-cell batteries with a holder, or a variable DC power supply if available), a known resistor (e.g., 100 Ω, 220 Ω, or a small filament bulb), an ammeter, a voltmeter, and connecting wires.
Procedure: Step 1: Draw the circuit diagram on the board: a series circuit with the power supply, ammeter, and resistor. Connect the voltmeter in parallel across the resistor.
Step 2: Guide students (or demonstrate) to assemble the circuit carefully, ensuring correct polarity for ammeter and voltmeter.
Step 3: Start with a low voltage (e.g., one battery). Read and record the current (I) from the ammeter and the voltage (V) from the voltmeter.
Step 4: Increase the voltage (e.g., add another battery in series, or adjust variable power supply). Record new I and V readings. Repeat for 3-4 different voltage levels.
Step 5: Instruct students to create a data table (Voltage, Current, Calculated Resistance (V/I)).
Step 6: Guide students to plot a graph of Voltage (V) on the y-axis against Current (I) on the x-axis.
Step 7: Discuss the expected outcome: a straight line passing through the origin, confirming direct proportionality. The slope of the graph represents the resistance.
Safety: Emphasize safety precautions when handling electrical components (e.g., avoid short circuits, do not touch live wires, handle batteries carefully).
Student Activities:
1. Participation and Discussion: Actively participate in the initial discussion about electricity and its uses in Nigeria. Ask questions for clarification during concept explanations. Engage with the water pipe analogy and try to draw parallels.
2. Note-Taking and Diagram Drawing: Take comprehensive notes on definitions, units, symbols, and measuring instruments. Draw the circuit diagrams for current and voltage measurement and for the Ohm's Law experiment. Copy the Ohm's Law triangle and practice using it.
3. Experiment (Hands-on or Observational): If equipment is available, students should work in groups to assemble the circuit for the Ohm's Law experiment under teacher supervision. If equipment is limited, students will keenly observe the teacher's demonstration, accurately record readings, and participate in data analysis. Construct the data table and plot the V-I graph. * Calculate the resistance (R = V/I) for each set of readings and compare the values. Discuss why they might not be Ohm's Law experiment. Copy the Ohm's Law triangle and practice using it.
3. Experiment (Hands-on or Observational): If equipment is available, students should work in groups to assemble the circuit for the Ohm's Law experiment under teacher supervision. If equipment is limited, students will keenly observe the teacher's demonstration, accurately record readings, and participate in data analysis. Construct the data table and plot the V-I graph. Calculate the resistance (R = V/I) for each set of readings and compare the values. Discuss why they might not be perfectly identical (experimental error).
4. Problem Solving: Work through the guided practice problems, attempting solutions before reviewing the provided answers. * Engage in independent practice problems. ---
Understanding the relationships between current, voltage, and resistance is crucial for navigating daily life in Nigeria, especially given varying power supply conditions and reliance on alternative energy sources. Household Electrical Safety and Appliance Usage: Application: Nigerians constantly use various electrical appliances (refrigerators, fans, televisions, chargers). Understanding Ohm's Law helps in appreciating why using the correct voltage (e.g., 230V from NEPA or generator) is important, and why using appliances designed for lower voltages on higher voltage sources can damage them (increased current flow due to lower resistance for the higher voltage). It also explains why an appliance with a higher resistance (e.g., a simple lamp) draws less current than a low-resistance appliance like an electric heater, which directly impacts electricity bills.
Local Context: Many homes rely on local electricians for wiring and repairs. Knowledge of these concepts helps homeowners communicate effectively with electricians about issues like 'low current' (which often means low voltage), frequent fuse blows (high current due to short circuits or overloads), or overheating appliances (faulty components with changing resistance).
Solar and Inverter Systems: Application: Due to unreliable grid power, solar panels and inverters are common in Nigeria. Ohm's Law is fundamental to designing and troubleshooting these systems. Knowing the voltage of solar panels (e.g., 12V, 24V), the current drawn by connected appliances, and their resistances allows users and technicians to correctly size batteries, inverters, and fuses. For example, knowing an appliance draws 5A at 12V (from an inverter) helps in calculating the battery capacity needed and the appropriate fuse rating to prevent damage.
Local Context: Many small businesses (e.g., barbing salons, provision stores) use small solar setups or inverters. Understanding these concepts helps them estimate operational costs, manage battery life, and make informed decisions when purchasing or maintaining their power systems.
Troubleshooting and Repair of Electronics: Application: Technicians and even individuals who repair their own devices (e.g., phone repairers, TV repairers) implicitly or explicitly use Ohm's Law. When a device isn't working, measuring voltage drops across components or checking for unexpected current draws can quickly pinpoint faulty parts that might have changed resistance (e.g., a burnt-out resistor, a short-circuit).
Local Context: Informal electronics repair shops are ubiquitous in Nigerian markets. These artisans, often self-taught, perform practical calculations related to voltage, current, and resistance to fix devices ranging from radios to generators. This lesson provides the theoretical foundation for their practical skills. ---