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Electric Circuits Overview

Sep 30, 2025

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Overview

This lesson focuses on key concepts in electric circuits for Grade 11 and 12 science students. Topics include Ohm's Law, circuit calculations, power, the cost of electricity, and an introduction to internal resistance. The session also emphasizes the importance of exam guidelines, correct units, and foundational understanding for success in both grades.

Exam Guidelines & Key Concepts

  • Exam guidelines outline all required definitions, formulas, and concepts for exams.
  • Both Grade 11 and 12 students must understand:
    • Ohm's Law
    • Series and parallel circuits
    • Power and energy calculations
    • (For some) Internal resistance and EMF
  • Teachers use these guidelines to set exam papers; Grade 11 content is also tested in Grade 12.
  • Always use correct units:
    • Charge: coulombs (C)
    • Current: amperes (A)
    • Voltage: volts (V)
    • Resistance: ohms (Ω)
    • Power: watts (W)
    • Energy: joules (J) or kilowatt-hours (kWh)

Ohm's Law & Resistance

  • Ohm’s Law: The potential difference (V) across a conductor is directly proportional to the current (I) through it, provided temperature is constant.
    • Formula: V = I × R
    • Rearranged: I = V / R or R = V / I
  • On a V vs. I graph:
    • A straight line through the origin indicates an ohmic conductor.
    • The gradient of a V vs. I graph is resistance (R).
    • For an I vs. V graph, the gradient is 1/R.
  • When stating relationships, specify the type (e.g., "directly proportional") and the constant variable (e.g., "at constant temperature").
  • Definitions and formulas from exam guidelines must be memorized and understood.

Series and Parallel Circuits

  • Series Circuits:
    • Current is the same throughout all components.
    • Voltage splits across each resistor; total voltage is the sum of voltages across each component.
  • Parallel Circuits:
    • Voltage is the same across all branches.
    • Current splits between branches; total current is the sum of branch currents.
  • Calculating resistance:
    • For resistors in parallel: 1/R_total = 1/R1 + 1/R2 + ...
    • For mixed circuits: calculate parallel resistance first, then add series resistances.
  • Understanding how current and voltage behave in different circuit arrangements is essential for solving problems.

Example Calculations

  • To find effective resistance:
    • Identify and solve for parallel combinations first.
    • Add any series resistors to the effective parallel resistance.
  • Use Ohm’s Law (I = V / R) to calculate total current.
  • For branch currents in parallel, use current division ratios:
    • The branch with lower resistance receives more current.
    • Use ratios or the current divider formula to split total current among branches.
  • Always show formulas and units in calculations to avoid losing marks.

Power and Cost of Electricity

  • Power Formulas:
    • P = V × I
    • P = I² × R
    • P = V² / R
    • P = Energy / time
  • Energy Calculations:
    • Energy (in kWh) = Power (in kW) × Time (in hours)
    • Convert power from watts to kilowatts (divide by 1000).
    • Convert time from minutes to hours (divide by 60).
  • Cost Calculation:
    • Cost = energy used (kWh) × tariff (cost per kWh)
    • Electricity is sold in kilowatt-hours; always match units to the tariff.
  • Example steps:
    1. Convert power and time to correct units.
    2. Calculate energy in kWh.
    3. Multiply by the tariff to find total cost.
  • Remember: kilowatt-hour (kWh) is a unit of energy, not power.

Internal Resistance & EMF

  • EMF (Electromotive Force): The maximum energy provided by a battery per unit charge.
    • When the switch is open (no current), a voltmeter across the battery reads the EMF.
    • When the switch is closed (current flows), the voltmeter reads the terminal voltage, which is less than the EMF due to internal resistance.
  • Internal Resistance (r): The resistance inside the battery that causes some energy to be lost as heat.
  • Key Formulas:
    • EMF = I(R + r), where R = external resistance, r = internal resistance, I = total current.
    • EMF = terminal voltage + lost volts (voltage across internal resistance).
    • Lost volts = EMF - terminal voltage = I × r
  • In circuit diagrams, internal resistance is shown as a small resistor inside the battery symbol.
  • When solving problems:
    • Calculate total external resistance first.
    • Use the EMF formula to solve for current or other unknowns.
    • Understand the difference between EMF, terminal voltage, and lost volts.

Key Terms & Definitions

  • Ohm's Law: V = IR; at constant temperature, voltage is proportional to current.
  • EMF: Maximum energy provided by a battery per coulomb of charge.
  • Internal Resistance: Resistance inside the battery, causing voltage loss.
  • Power (P): Rate at which energy is used or transferred (P = VI).
  • Kilowatt-hour (kWh): Unit of energy; one kilowatt used for one hour.
  • Series Circuit: Components connected end-to-end; same current flows through all.
  • Parallel Circuit: Components connected across the same two points; same voltage across each branch.
  • Terminal Voltage: The voltage measured across the battery when current is flowing (less than EMF due to internal resistance).
  • Lost Volts: The voltage lost across the internal resistance of the battery.

Action Items / Next Steps

  • Review and memorize all key definitions, formulas, and units for each circuit component.
  • Practice calculating total resistance and current in both series, parallel, and mixed circuits.
  • Work through examples involving power and the cost of electricity, ensuring correct unit conversions.
  • Grade 12s: Focus on problems involving EMF and internal resistance, including identifying lost volts and terminal voltage.
  • Download or request summarized notes and formula sheets if available (see provided bio link).
  • Comment or reach out with specific topics or questions for future lessons or additional resources.

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