Lesson Notes By Weeks and Term v3 - Senior Secondary 3
Electric Field
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Electric Field
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Subject: Physics
Class: Senior Secondary 3
Term: 1st Term
Week: 1
Theme: Fields At Rest And In Motion
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Identify all the component parts of simple cell amd accumulator Solve problems in volving series and parallel connections of resistors and cells Convert galvanometer to an ammeter and to a voltmeter State and demonstrate the condition for a balanced wheatstone bridge circuit and deduce the condition for balance meter bridge circuit State and demonstrate the condition for a balanced whetdtone bridge circuit and deduce the condition for balanced meter bridge circuit explain the basic principle of the potentimeter circuit Explain the conditions under which liquids and gases conduct electricity Explain the behaviour of charges or charge centres in liquids and gases in the electric field...
Simple Cell (Primary Cell): Definition: An electrochemical device that converts chemical energy into electrical energy through an irreversible chemical reaction. Once the chemicals are depleted, the cell cannot be recharged.
Components: Positive Electrode (Anode): The terminal from which current flows out of the cell (often carbon/copper).
Negative Electrode (Cathode): The terminal into which current flows (often zinc).
Electrolyte: A chemical substance (liquid or paste) that conducts electricity through the movement of ions between the electrodes (e.g., dilute sulphuric acid, ammonium chloride paste).
Container: Holds the components.
Separator: Prevents direct contact between electrodes.
Examples: Dry cell (Leclanché cell), Daniell cell. Accumulator (Secondary Cell / Rechargeable Battery): Definition: An electrochemical device where the chemical reactions are reversible. It can be recharged by passing an external current through it, converting electrical energy back into chemical energy for later use.
Components: Similar to a simple cell, but designed for reversibility.
Positive Plate: Lead (IV) oxide (PbO2).
Negative Plate: Pure lead (Pb).
Electrolyte: Dilute sulphuric acid (H2SO4).
Container: Acid-resistant material.
Types: Lead-acid accumulator (common in vehicles), Nickel-Cadmium (Ni-Cd), Nickel-Metal Hydride (Ni-MH), Lithium-ion (Li-ion).
Difference: Primary cells are single-use; secondary cells are rechargeable. 2.1.1 Simple Cells (Primary Cells): Description: These convert chemical energy into electrical energy through an irreversible chemical reaction. They cannot be recharged once the chemical reactants are depleted.
Component Parts: Anode (Positive Electrode): Typically a carbon rod (in a dry cell) or a copper plate (in a Daniell cell). It is where oxidation occurs, losing electrons.
Cathode (Negative Electrode): Often a zinc casing or plate. It is where reduction occurs, gaining electrons.
Electrolyte: A chemical solution or paste that allows ions to move between the electrodes. Examples include ammonium chloride paste (dry cell) or dilute sulphuric acid (voltaic cell). The electrolyte completes the internal circuit, providing a medium for charge carriers (ions) to move.
Depolarizer: (e.g., manganese dioxide in a dry cell) Prevents the buildup of hydrogen gas bubbles on the positive electrode, which would otherwise increase internal resistance and reduce EM
F. Container: Holds all components and prevents leakage.
Function: To provide a continuous flow of electrons (current) through an external circuit by maintaining a potential difference (EMF) generated by the chemical reaction. 2.1.2 Accumulators (Secondary Cells / Rechargeable Batteries): Description: These are electrochemical cells whose chemical reactions are reversible. They can be recharged by passing an electric current through them in the reverse direction, converting electrical energy back into chemical energy for later use. Component Parts (e.g., Lead-Acid Accumulator): Positive Plate: Made of lead (IV) oxide (PbO2) deposited on a lead grid.
Negative Plate: Made of pure spongy lead (Pb) also on a lead grid.
Electrolyte: Dilute sulphuric acid (H2SO4) with a specific gravity typically around 1.25 to 1.28 when fully charged. This acid provides ions (H+ and SO42−) for conduction.
Separators: Porous insulators placed between positive and negative plates to prevent short-circuiting while allowing electrolyte circulation.
Container: Made of acid-resistant material (e.g., hard rubber or plastic) with vents to release gases during charging.
Function: To store electrical energy as chemical energy during charging and convert it back to electrical energy during discharge.
Relevance (Nigeria): Car batteries (lead-acid) are ubiquitous. Inverters/UPS systems use deep-cycle accumulators to provide backup power, especially important during power outages from the national grid. 2.2.1 Resistors Series Connection: Resistors are connected end-to-end, forming a single path for current.
Current: Same through all resistors (I_total = I1 = I2 = ...).
Voltage: Divides across the resistors (V_total = V1 + V2 + ...). Equivalent Resistance (R_eq): R_eq = R1 + R2 + R3 + ...
Application: To increase total resistance. Worked
Example: Three resistors, 5 Ω, 10 Ω, and 15 Ω, are connected in series to a 30 V battery. (a) Calculate the total resistance. (b) Calculate the total current flowing in the circuit.
Solution: (a) R_eq = R1 + R2 + R3 = 5 Ω + 10 Ω + 15 Ω = 30 Ω (b) I_total = V_total / R_eq = 30 V / 30 Ω = 1 A Parallel Connection: Resistors are connected across the same two points, providing multiple paths for current.
Voltage: Same across all resistors (V_total = V1 = V2 = ...).
Current: Divides among the resistors (I_total = I1 + I2 + ...). Equivalent Resistance (R_eq): 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...
Application: To decrease total resistance, or to allow components to operate independently. Worked
Example: Two resistors, 12 Ω and 6 Ω, are connected in parallel to a 12 V power supply. (a) Calculate the total resistance. (b) Calculate the total current drawn from the supply.
Solution: (a) 1/R_eq = 1/12 Ω + 1/6 Ω = (1 + 2)/12 Ω = 3/12 Ω = 1/4 Ω R_eq = 4 Ω (b) I_total = V_total / R_eq = 12 V / 4 Ω = 3 A 2.2.2 Cells Series Connection: Cells are connected positive terminal to negative terminal. Total EMF (E_total): E_total = E1 + E2 + E3 + ... (if connected aiding each other). If some cells are connected in opposition, their EMFs are subtracted. Total Internal Resistance (r_total): r_total = r1 + r2 + r3 + ...
Application: To obtain a higher voltage. Worked
Example: Three cells, each with EMF 1.5 V and internal resistance 0.5 Ω, are connected in series. Calculate the total EMF and total internal resistance.
Solution: E_total = 1.5 V + 1.5 V + 1.5 V = 4.5 V r_total = 0.5 Ω + 0.5 Ω + 0.5 Ω = 1.5 Ω Parallel Connection: Cells are connected positive to positive, negative to negative.
Condition: Cells must have the same EMF for efficient parallel operation to avoid circulating currents. Total EMF (E_total): E_total = E (if all cells have the same EMF E). Total Internal Resistance (r_total): 1/r_total = 1/r1 + 1/r2 + 1/r3 + ... For 'n' identical cells, r_total = r/n.
Application: To obtain a higher current capacity (longer lasting), or to reduce the overall internal resistance. Worked
Example: Two identical cells, each with EMF 1.5 V and internal resistance 0.3 Ω, are connected in parallel. Calculate the total EMF and total internal resistance.
Solution: E_total = 1.5 V (since EMFs are identical) 1/r_total = 1/0.3 Ω + 1/0.3 Ω = 2/0.3 Ω r_total = 0.3/2 Ω = 0.15 Ω The way components are connected in a circuit significantly affects the overall current and voltage distribution, which are direct consequences of the electric field established in the circuit. 2.2.1 Resistors Series Connection: Resistors (R1, R2, R3, ...) are connected end-to-end.
Current (I): The same current flows through all resistors: I_total = I1 = I2 = I
3. Voltage (V): The total voltage across the combination is the sum of the individual voltages: V_total = V1 + V2 + V
3. Equivalent Resistance (R_eq): Increases the total resistance. R_eq = R1 + R2 + R3 + ... Practical
Example: Christmas lights (old type), which go out entirely if one bulb fuses.
Worked Example 1: An electrical appliance with an effective resistance of 20 Ω is connected in series with a 5 Ω resistor to a 100 V supply. (a) Calculate the equivalent resistance of the circuit. (b) Determine the total current flowing from the supply.
Solution: (a) R_eq = R1 + R2 = 20 Ω + 5 Ω = 25 Ω (b) I_total = V_total / R_eq = 100 V / 25 Ω = 4 A Parallel Connection: Resistors (R1, R2, R3, ...) are connected across the same two points, providing multiple paths for current.
Voltage (V): The voltage across each resistor is the same: V_total = V1 = V2 = V
3. Current (I): The total current is the sum of the currents through each resistor: I_total = I1 + I2 + I
3. Equivalent Resistance (R_eq): Decreases the total resistance. 1/R_eq = 1/R1 + 1/R2 + 1/R3 + ...
For two resistors: R_eq = (R1 * R2) / (R1 + R2) Practical
Example: Household wiring where each appliance (fan, light, TV) receives the full mains voltage and operates independently.
Worked Example 2: Two heating coils of 30 Ω and 60 Ω are connected in parallel to a 240 V mains supply (common in Nigeria). (a) Calculate their equivalent resistance. (b) Find the total current drawn from the supply.
Solution: (a) 1/R_eq = 1/30 Ω + 1/60 Ω = (2 + 1)/60 Ω = 3/60 Ω = 1/20 Ω R_eq = 20 Ω (b) I_total = V_total / R_eq = 240 V / 20 Ω = 12 A 2.2.2 Cells Series Connection: Cells are connected positive terminal to negative terminal. Total EMF (E_total): Sum of individual EMFs. If 'n' identical cells (EMF E) are connected, E_total = n
E. If cells oppose, subtract EMFs. Total Internal Resistance (r_total): Sum of individual internal resistances: r_total = r1 + r2 + r3 + ...
Application: To achieve higher total voltage. (e.g., linking dry cells in series in a flashlight to increase brightness).
Parallel Connection: Cells are connected positive to positive, negative to negative.
Condition: Cells must ideally have the same EMF to prevent circulating currents and damage. Total EMF (E_total): Remains the same as a single cell: E_total =
E. Total Internal Resistance (r_total): 1/r_total = 1/r1 + 1/r2 + 1/r3 + ... (for identical cells, r_total = r/n).
Application: To increase the current capacity and extend the battery's lifespan, useful for heavy current applications. (e.g., car batteries consist of multiple cells in series-parallel configurations).
Worked Example 3: A battery is formed by connecting five identical cells, each with an EMF of 1.5 V and an internal resistance of 0.2 Ω, in series. This battery is then connected to an external load of 9 Ω. (a) Calculate the total EMF of the battery. (b) Calculate the total internal resistance of the battery. (c) Calculate the current flowing through the external load.
Solution: (a) E_total = 5 * 1.5 V = 7.5 V (b) r_total = 5 * 0.2 Ω = 1.0 Ω (c) Total circuit resistance = R_load + r_total = 9 Ω + 1.0 Ω = 10 Ω Current (I) = E_total / (R_load + r_total) = 7.5 V / 10 Ω = 0.75 A
Power Backup Systems (Inverters/UPS) in Nigerian Homes and Businesses: The understanding of accumulators (P.O. 1) and series/parallel connections of cells (P.O. 2) is directly applicable here. In Nigeria, erratic power supply from the national grid necessitates the widespread use of inverters and UPS systems. These systems rely on banks of deep-cycle accumulators (often lead-acid batteries) connected in series and parallel to provide desired voltage and current capacity during outages. The electric field established by these batteries drives current to power appliances. Electroplating and Metal Fabrication Industries: The principles of electrical conduction through liquids (P.O. 7, 8, 9) are fundamental to electroplating, which is used by artisans and industries in Nigeria for aesthetic purposes (e.g., gold-plating jewelry, chrome plating car parts) and for corrosion protection of metal components. For instance, in the motor spare parts industry in Aba or Lagos, electroplating extends the lifespan of metal parts, saving costs and enhancing product quality. The applied electric field in the electrolytic cell forces ions to deposit on the desired object.
Telecommunications and Electronic Gadgets: All modern electronic devices, from mobile phones (ubiquitous in Nigeria) to radio transmitters and receivers, extensively use capacitors (P.O. 12, 13, 14) and operate based on the principles of electric fields and potentials (P.O. 10, 11). Capacitors store energy, filter signals, and stabilize voltages in circuits. The understanding of electric fields and potential is crucial for designing and troubleshooting these essential communication technologies that connect Nigerians daily. ---