Chapter 8: Electricity

Overview

Electricity is one of the most fundamental topics in physics, governing countless aspects of modern life. This chapter covers electric current, potential difference, resistance, circuit analysis, and electrical energy. Understanding these concepts is essential for comprehending how electrical devices work, how circuits function, and how electrical energy is converted and used in various applications.

Learning Objectives

After completing this chapter, you will be able to:

• Understand and calculate electric current and potential difference
• Apply Ohm's Law to analyze electrical circuits
• Distinguish between ohmic and non-ohmic conductors
• Analyze series and parallel circuits
• Calculate electromotive force and internal resistance
• Solve problems involving electrical energy and power

Current and Potential Difference

Main Concept

Electric current is the rate of flow of electric charge. Potential difference (voltage) is the work done per unit charge to move charge between two points.

Key Principles

• Current flows from positive terminal to negative terminal (conventional current)
• Electrons flow from negative to positive
• Current is measured in Amperes (A)
• Potential difference is measured in Volts (V)

Key Formulas

Current, I:

$$I = \frac{Q}{t}$$

Potential Difference, V:

$$V = \frac{W}{Q} \text{ or } V = \frac{E}{Q}$$

Where:

• I = Current in Amperes (A)
• Q = Charge in Coulombs (C)
• t = Time in seconds (s)
• V = Potential difference in Volts (V)
• W or E = Work or Energy in Joules (J)

Important Terms

• Electric Field: Region where electric charge experiences electric force
• Conventional Current: Flow from positive to negative
• Electron Flow: Actual flow of electrons from negative to positive

Current Direction Clarification

It's important to understand that:

• Conventional current: Positive to negative (historical convention)
• Electron flow: Negative to positive (actual electron movement)
• Current direction: Always follows conventional current in circuit analysis

Electric Current Flow Diagram

Current and Potential Relationship

Resistance

Main Concept

Resistance is the ratio of potential difference across a conductor to the current flowing through it. It opposes the flow of current.

Key Principles

• Ohm's Law: The current through an ohmic conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant.

Key Formulas

Resistance, R:

$$R = \frac{V}{I}$$

Resistivity, ρ:

$$R = \frac{ρL}{A}$$

Where:

• R = Resistance in Ohms (Ω)
• ρ = Resistivity
• L = Length of conductor
• A = Cross-sectional area

Important Terms

• Ohmic Conductor: Conductor that obeys Ohm's Law (V-I graph is straight line through origin)
• Non-ohmic Conductor: Conductor that doesn't obey Ohm's Law (e.g., diode, filament bulb)
• Superconductor: Material with zero resistance below certain critical temperature

Resistance vs Resistivity

Material Resistivity Comparison

Ohmic vs Non-Ohmic Behavior

Temperature Effect on Resistance

Most conductors have resistance that changes with temperature:

• Metals: Resistance increases with temperature (positive temperature coefficient)
• Semiconductors: Resistance decreases with temperature (negative temperature coefficient)
• Superconductors: Resistance drops to zero below critical temperature

Temperature vs Resistance Graph

Superconductor Applications

Series and Parallel Circuits

Main Concept

Circuit components can be connected in series or parallel, which affects current, voltage, and effective resistance.

Key Principles

Series Circuit:

• Current is the same through each component: I_total = $I_1$ = $I_2$ = ...
• Voltage is shared: V_total = $V_1$ + $V_2$ + ...
• Effective resistance is sum: R_eff = $R_1$ + $R_2$ + ...

Parallel Circuit:

• Current is shared: I_total = $I_1$ + $I_2$ + ...
• Voltage is same across each branch: V_total = $V_1$ = $V_2$ = ...
• Effective resistance: 1/R_eff = 1/$R_1$ + 1/$R_2$ + ...

Key Formulas

All formulas above for series and parallel circuits.

Important Terms

• Voltage Divider: Series circuit used to divide source voltage
• Current Divider: Parallel circuit used to divide total current

Circuit Comparison Table

Series vs Parallel Circuit Diagrams

Current and Voltage Distribution

Worked Example

Problem: Three resistors of 2Ω, 3Ω, and 6Ω are connected in parallel to a 12V battery. Calculate: a) The effective resistance b) The total current c) The current through each resistor

Solution: a) Effective resistance:

$$\frac{1}{R_eff} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} = \frac{3}{6} + \frac{2}{6} + \frac{1}{6} = \frac{6}{6} = 1$$ $$R_eff = 1Ω$$

b) Total current:

$$I_total = \frac{V}{R_eff} = \frac{12}{1} = 12A$$

c) Current through each resistor:

$$I_1 = \frac{V}{R_1} = \frac{12}{2} = 6A$$ $$I_2 = \frac{V}{R_2} = \frac{12}{3} = 4A$$ $$I_3 = \frac{V}{R_3} = \frac{12}{6} = 2A$$

Answer: a) 1Ω, b) 12A, c) 6A, 4A, 2A

Electromotive Force (EMF) and Internal Resistance

Main Concept

Electromotive force (e.m.f., ε) is the total energy supplied by a source (like a battery) to move one unit charge around a complete circuit. Internal resistance (r) is the resistance within the source itself.

Key Principles

• When current flows, some voltage is "lost" across internal resistance. This is called "lost volts".
• Potential difference across battery terminals (V) is always less than e.m.f. (ε) when circuit is complete. V = ε - Ir.

Key Formulas

e.m.f., ε:

$$ε = \frac{E}{Q}$$

Relationship between e.m.f. and V:

$$ε = V + Ir$$

Circuit Current:

$$I = \frac{ε}{R + r}$$

Where:

• ε = Electromotive force in Volts (V)
• r = Internal resistance in Ohms (Ω)
• R = External resistance
• Ir = Lost volts

Battery Internal Resistance Model

Terminal Voltage vs Load

Battery Characteristics Graph

Battery Testing Methods

Electrical Energy and Power

Main Concept

Electrical energy is the capacity of electric current to do work. Electrical power is the rate at which electrical energy is converted to other forms of energy.

Key Principles

• Electrical energy can be converted to heat, light, sound, or mechanical energy
• Power is measured in Watts (W)
• Energy is measured in Joules (J) or kilowatt-hours (kWh) for commercial use

Key Formulas

Electrical Energy, E:

• E = VQ
• E = VIt
• E = $I^2$Rt
• E = ($V^2$/R)t

Electrical Power, P:

• P = E/t
• P = VI
• P = $I^2$R
• P = $V^2$/R

Where:

• E = Energy in Joules (J)
• P = Power in Watts (W)

Important Terms

• Kilowatt-hour (kWh): Commercial unit of electrical energy. 1 kWh = 3.6 × 10⁶ J
• Efficiency: (Power output / Power input) × 100%

Power Dissipation in Resistors

Power Dissipation Modes

Energy Cost Calculation

Cost of Electricity:

• Cost = Energy (kWh) × Tariff (RM/kWh)

Example: A 100W lamp used for 5 hours daily for 30 days:

• Energy = 0.1 kW × 5 h/day × 30 days = 15 kWh
• Cost = 15 kWh × RM 0.50/kWh = RM 7.50

Electricity Tariff Analysis

Power Rating and Selection

SPM Exam Tips

Common Mistakes to Avoid

1. Current Direction: Remember conventional current flows positive to negative
2. Ohm's Law: Applies only to ohmic conductors at constant temperature
3. Circuit Analysis: Draw clear circuit diagrams before solving
4. Units: Use consistent units (Volts, Amperes, Ohms, Watts)
5. Internal Resistance: Remember terminal voltage is less than e.m.f. when current flows

Problem-Solving Strategies

1. Identify Circuit Type: Determine if series, parallel, or combination
2. Label Components: Assign currents and voltages clearly
3. Apply Relevant Laws: Use Ohm's Law, Kirchhoff's laws, or circuit rules
4. Solve Step by Step: Find one unknown at a time
5. Check Units: Ensure all units are consistent

Important Formula Summary

Practical Applications

Real-World Examples

1. Household Wiring: Series and parallel circuits for different appliances
2. Battery Design: Internal resistance affects battery performance
3. Electrical Safety: Fuses and circuit breakers for protection
4. Energy Efficiency: Choosing appropriate power ratings for devices
5. Renewable Energy: Solar panels and wind generators

Safety Considerations

• Overloading: Circuits can overheat if too much current flows
• Short Circuits: Can cause fires if not properly protected
• Electrical Shock: Dangerous currents through human body
• Proper Grounding: Prevents electrical hazards

Circuit Analysis Techniques

Kirchhoff's Laws

First Law (Current Law):

• Sum of currents entering a junction equals sum of currents leaving
• ΣI_in = ΣI_out

Second Law (Voltage Law):

• Sum of e.m.f.'s equals sum of potential drops in a closed loop
• Σε = ΣIR

Kirchhoff's Laws Application

Circuit Solving Process

Complex Circuit Analysis

Bridge Circuit Applications

Measurement Techniques

Summary

This chapter covered essential electricity concepts:

• Current and Voltage: Fundamental quantities in electric circuits
• Resistance: Ohm's Law and resistivity
• Circuit Analysis: Series and parallel circuits
• EMF and Internal Resistance: Real battery behavior
• Electrical Energy and Power: Energy conversion and usage

Master these concepts to understand electrical systems, circuit design, and energy management - fundamental to modern technology and everyday life.

Practice Questions

1. A current of 0.5A flows through a resistor for 10 minutes. Calculate the charge that flows through the resistor.

2. Three resistors of 4Ω, 6Ω, and 12Ω are connected in series across a 24V supply. Calculate: a) The total resistance b) The current through the circuit c) The voltage across each resistor

3. A battery with e.m.f. 12V and internal resistance 0.5Ω is connected to an external resistor of 5.5Ω. Calculate: a) The current in the circuit b) The terminal voltage of the battery

4. A 60W, 240V electric lamp is left switched on for 8 hours. Calculate: a) The current it draws b) The electrical energy consumed in kWh c) The cost if electricity costs RM 0.60 per kWh

5. Explain the difference between e.m.f. and terminal voltage of a battery.

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• Chapter 7: Pressure
• Chapter 9: Electromagnetism