Everything you need for the Leaving Cert — static charge, current, circuits, magnetism and electromagnetic induction — explained simply with worked examples.
💡 How to use this guide: Work through each section in order. Every topic has simple explanations, key definitions to learn word-for-word, formulas with examples, and worked calculations. Test yourself with the quizzes at the end of each booklet!
Booklet I — Static Electricity
⚡ Static Electricity & Charge
Charge is the fundamental property behind all of electricity. Understanding static charge unlocks everything else.
What is Charge?
Every atom contains protons (+) and electrons (−). Normally they balance, and the atom is neutral. But electrons can be transferred between objects by rubbing, contact, or induction.
If a charged object is connected to the earth (ground), the excess charge flows away to earth and the object becomes neutral.
This is why buildings have lightning conductors — they provide a safe path for the charge from a lightning strike to flow into the ground instead of through the building.
🔌 Charging by Induction
You can charge a conductor WITHOUT touching it with a charged object. This is called charging by induction.
🎯 Exam: 4 steps for charging by induction (learn these in order!)
1. Bring a charged rod CLOSE TO (but not touching) the conductor
2. Earth the conductor (touch it with your finger or connect an earth wire)
3. Remove your finger/earth connection
4. Remove the rod
Result: conductor is charged OPPOSITE to the rod!
⚡ Applications of Static Electricity
Precipitators: Remove smoke/dust particles from factory chimneys using static charge
Photocopiers: Use static charge to pick up and place toner ink
Van de Graaff generator: Builds up large amounts of static charge on a metal dome
⚠️ Hazards
Explosions in flour mills — static spark ignites fine dust particles
Explosions when fuelling aircraft — fuel flowing through pipes creates static
Damage to electronic circuits — static discharge destroys tiny components
Booklet I — Static Electricity
🔮 The Gold Leaf Electroscope
The gold leaf electroscope (GLE) is the simplest device for detecting whether something is charged.
🔎 How it Works
The GLE has a metal cap connected to a thin strip of gold leaf inside a glass case. When charge is placed on the cap, it spreads to the leaf which then stands away from the metal rod — because both have the same charge and like charges repel!
Leaves together
Uncharged
No excess charge → no repulsion → leaf hangs down
Leaves apart
Charged!
Either + or − charge → same charges on leaf and rod → repulsion
🎯 Functions of the GLE
To detect whether an object is charged
To distinguish between positive and negative charge
🧠 How to tell + from −: Charge the GLE with a known positive charge so the leaves diverge. Now bring your unknown object near the cap. If the leaves diverge MORE → object is positive. If they collapse → object is negative (it's attracting the charge up to the cap, removing charge from the leaves).
Earthing the GLE
If you touch the cap of a charged GLE with your finger, the leaves collapse. The charge flows through your body to earth — the GLE becomes neutral. This is earthing in action!
Booklet I — Static Electricity
📐 Coulomb's Law
How strong is the force between two charged objects? Coulomb worked out the exact mathematical relationship.
📖 Coulomb's Law
The force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
⚠️ Coulomb's Law Formula
F = Q₁Q₂ / (4πεd²)
F = electrostatic force (N) Q₁, Q₂ = the two charges (coulombs, C) ε = permittivity of the medium (for vacuum/air: ε₀ = 8.9 × 10⁻¹² F m⁻¹) d = distance between the centres of the charges (m)
🧠 This is an INVERSE SQUARE LAW — just like gravity! If you double the distance, the force becomes 4× smaller. If you halve the distance, the force becomes 4× bigger.
🆚 Coulomb's Force vs Gravity
Property
Coulomb's Force
Gravitational Force
Type
Can be repulsive or attractive
Always attractive
Magnitude
MUCH larger (10³⁶ × bigger)
Very small
Depends on
Charge × charge, 1/d²
Mass × mass, 1/d²
Booklet I — Static Electricity
🌐 Electric Fields & Field Strength
An electric field is the region around a charged object where other charges feel a force. We can map these fields using field lines.
📖 Electric Field
An electric field is a region of space where an electric charge experiences an electrostatic force.
📖 Electric Field Strength (E)
Electric field strength at a point is the force per unit charge at that point. E = F/Q. Unit: N C⁻¹.
⚠️ Two Formulas for E
E = F/Q (use when given force and charge)
E = Q/(4πεd²) (use when given distance)
Tip: If the question gives a distance (d), use the second equation. If it gives a force, use the first.
🗺️ Electric Field Lines — Rules
Field lines go FROM positive charges TO negative charges
The closer together the lines, the stronger the field
Field lines never cross each other
The direction at any point = direction of force on a positive test charge there
⚡ E at a Distance from a Sphere
If asked about the field at a point a distance d from the surface of a sphere of radius r, the total distance to use in the formula is d + r (distance to the centre, not the surface).
🎯 Common exam mistake: Always add the sphere's radius! The formula uses distance from the CENTRE of the sphere, not from its surface.
⚡ Distribution of Charge on a Conductor
All static charge resides on the OUTSIDE of a conductor (like charges repel to maximum separation)
Charge is most dense at pointed/sharp areas of a conductor
Point discharge: When charge density is very high at a point, it "leaks off" — ionising the air. This is how lightning conductors work!
🌩️ Demonstrating Electric Field Patterns
Set up two electrodes in a dish of castor oil. Sprinkle semolina powder on the surface. When you switch on the high-voltage DC supply, the semolina aligns with the electric field lines, revealing the pattern.
🎯 Exam tips: You MUST say "high voltage DC supply". You MUST specify semolina (not iron filings — those are for magnetic fields!)
Booklet I — Potential Difference
🔋 Potential Difference & The Volt
Voltage (potential difference) is the "push" that drives charge around a circuit. Understanding it is crucial for everything in electricity.
📖 Potential Difference (p.d.)
The potential difference between two points is the work done when a charge of 1 coulomb moves from one point to the other.
📖 The Volt
The potential difference between two points is 1 volt if 1 joule of work is done when bringing a charge of 1 coulomb from one point to the other.
Formula — Work, Charge & Voltage
W = V × Q
W = work done (J) V = potential difference (V) Q = charge (C)
🧠 Simple explanation: Voltage is the energy per coulomb of charge. A 9V battery gives 9 joules of energy to every coulomb of charge that passes through it. More voltage = more energy per charge = bigger "push" around the circuit.
📖 Potential at a Point
The potential at a point is the work done in bringing a positive charge from that point to earth.
Booklet I — Capacitance
💾 Capacitors & Capacitance
A capacitor stores separated charge — like a tiny rechargeable battery. They're used in camera flashes, defibrillators, and touchscreens.
📖 Capacitance
The capacitance of a conductor is the ratio of the charge on the conductor to its potential (voltage). C = Q/V. Unit: farad (F).
⚠️ Capacitance Formula
C = Q / V
C = capacitance (F) Q = charge stored (C) V = voltage across capacitor (V)
🔲 Parallel Plate Capacitor
A parallel plate capacitor consists of two flat metal plates facing each other. Capacitance depends on three things:
Parallel Plate Capacitor Formula
C = εA / d
ε = permittivity of material between plates (F m⁻¹) A = overlap area of the plates (m²) d = distance between the plates (m)
Increase area A
C ↑ increases
More plate overlap = more capacitance
Increase gap d
C ↓ decreases
Larger gap = less capacitance
Insert dielectric
C ↑ increases
Material between plates raises ε → more capacitance
⚡ Energy Stored in a Capacitor
⚠️ Energy Stored
W = ½CV²
W = energy stored (J) C = capacitance (F) V = voltage (V)
🎯 Defibrillators use capacitors! A 64 μF capacitor charged to 2500V stores: W = ½(64×10⁻⁶)(2500)² = 200 J — enough to restart a heart. The capacitor dumps this energy in milliseconds.
Applications of Capacitors
Camera flash (stores energy, releases it quickly)
Defibrillators (stores then releases large energy pulse)
Radio tuning (changing area changes capacitance → selects frequency)
Touchscreens (finger acts as a plate of a capacitor)
Allows AC to pass but BLOCKS DC
Booklet I — Worked Examples
📐 Calculations: Booklet I
Coulomb's law, electric field strength and capacitance — step by step.
Example 1 — Coulomb's Law
Q: Two spheres, each charged to +3 μC, are 8 cm apart in a vacuum. Find the repulsive force. (ε₀ = 8.9×10⁻¹² F m⁻¹)
Write down values
Q₁=Q₂=3×10⁻⁶ C, d=0.08 m, ε₀=8.9×10⁻¹² F m⁻¹
Use F = Q₁Q₂ / (4πε₀d²)
F = (3×10⁻⁶)(3×10⁻⁶) / [4π(8.9×10⁻¹²)(0.08)²] F = 9×10⁻¹² / [7.16×10⁻¹³] F = 12.57 N
✅ Force = 12.57 N (repulsive, as both are positive)
Example 2 — Electric Field Strength near a Sphere
Q: A metal sphere of diameter 5 cm holds charge −6 μC. Find E at 3 cm from the surface.
Total distance from centre
d = (3 cm surface) + (2.5 cm radius) = 5.5 cm = 0.055 m
E = Q / (4πεd²)
E = (6×10⁻⁶) / [4π(8.9×10⁻¹²)(0.055)²] E = 1.78×10⁷ N C⁻¹
✅ E = 1.78×10⁷ N C⁻¹ (directed towards sphere — it's negative)
Example 3 — Capacitance
Q: Capacitor has charge 0.025 C and p.d. = 250 V. Find capacitance.
C = Q/V
C = 0.025 / 250 = 1×10⁻⁴ F = 100 μF
✅ C = 100 μF = 1×10⁻⁴ F
Example 4 — Energy in a Capacitor (Defibrillator)
Q: A 64 μF capacitor is charged to 2500 V. Find (i) charge stored, (ii) energy stored.
Part (i): Q = CV
Q = (64×10⁻⁶)(2500) = 0.16 C
Part (ii): W = ½CV²
W = ½(64×10⁻⁶)(2500)² = ½(64×10⁻⁶)(6.25×10⁶) = 200 J
✅ Charge = 0.16 C, Energy = 200 J
Booklet I — Quiz
✅ Quiz: Booklet I
Test yourself on Static Electricity, Electric Fields and Capacitance!
Booklet II — Current Electricity
🔌 Current & Charge
Electric current is charge moving through a conductor. The faster it moves and the more charge there is, the bigger the current.
📖 Electric Current
Electric current is a measure of the rate of flow of charge. I = Q/t. Unit: ampere (A).
Formula — Current
I = Q / t Q = It
I = current (A) Q = charge (C) t = time (s) 1 ampere = 1 coulomb per second
Rubber, plastic, glass. No free electrons. Used to safely cover wires.
🔄 Conventional Current
Conventional current flows from the positive to the negative terminal (as if positive charges are moving). In reality, it's the electrons (negative) that move from negative to positive. Thank you Benjamin Franklin for this historical confusion!
📊 Measuring Current & Voltage
Ammeter
IN SERIES
Connected in the circuit so ALL the current flows through it. Never in parallel — it would short circuit!
Voltmeter
IN PARALLEL
Connected across the component being measured. Never in series — it has very high resistance.
Power, Voltage and Current
⚠️ Electrical Power
P = VI
P = power (W) V = voltage (V) I = current (A)
Booklet II — Current Electricity
⚙️ Resistance & Ohm's Law
Resistance is what fights against current flow. Every material has a different resistance — and some depend on temperature!
📖 Resistance
The resistance of a conductor is the ratio of the potential difference across it to the current flowing through it. R = V/I. Unit: ohm (Ω).
📖 Ohm's Law
The current flowing through a conductor is directly proportional to the potential difference across it, assuming constant temperature.
⚠️ Ohm's Law Formula
V = IR R = V/I I = V/R
V = voltage/p.d. (V) I = current (A) R = resistance (Ω)
⚠️ Important: Ohm's Law only applies to OHMIC conductors (like metal wires at constant temperature). Filament bulbs, semiconductors and ionic solutions do NOT obey Ohm's Law because their resistance changes with temperature or other factors.
📈 V-I Graphs for Different Conductors
Conductor
Shape of V-I graph
Reason
Metallic conductor
Straight line through origin
Ohmic — constant resistance
Filament bulb
Curves (gets less steep)
Heats up → resistance increases → current rises less
Copper in CuSO₄ (active)
Straight line through origin
Copper ions continuously replaced
Semiconductor (diode)
Exponential curve
Resistance changes drastically with voltage
Booklet II — Current Electricity
🔗 Series & Parallel Circuits
Two ways to connect components — and they behave very differently. Master the 3-step method and you can solve any circuit!
📏 Series vs Parallel
Series Circuit
One path
• Current SAME everywhere • Voltages ADD up • R_total = R₁ + R₂ + R₃
Parallel Circuit
Multiple paths
• Voltage SAME across each branch • Currents ADD up • 1/R_total = 1/R₁ + 1/R₂
🪄 The 3-Step Method for Circuit Problems
Step 1 — Find TOTAL resistance (add series resistors, use 1/R formula for parallel) Step 2 — Find TOTAL voltage (usually given directly) Step 3 — Find TOTAL current: I_total = V_total / R_total
Then use V=IR for individual components (using the correct V and I for THAT component).
🌉 The Wheatstone Bridge
Four resistors connected in a diamond pattern. When the bridge is "balanced" (no current through the galvanometer in the middle), the following relationship holds:
Wheatstone Bridge (balanced)
R₁/R₂ = R₃/R₄
Used to find an unknown resistance if three others are known. Applications: temperature sensors, strain gauges — when temperature changes, balance is upset → current flows → triggers alarm
🎚️ Potential Divider
Two resistors in series share the total voltage proportionally to their resistances. If R₂ is 4× larger than R₁, then V₂ is 4× larger than V₁. A potentiometer (variable resistor) acts as an adjustable potential divider.
Booklet II — Current Electricity
🧱 Resistivity
Not all materials resist current equally. Resistivity tells us the inherent resistance of a material, independent of size or shape.
📖 Resistivity
Resistivity is defined as the resistance of a cube of material of side one metre (or: resistance per unit length per unit area). Unit: Ω m.
⚠️ Resistivity Formula
R = ρL / A
R = resistance (Ω) ρ (rho) = resistivity (Ω m) L = length of wire (m) A = cross-sectional area (m²)
For a wire: A = πr² (where r = radius of wire)
🧠 Key relationships (for a wire):
Resistance ∝ length (double the length → double the resistance)
Resistance ∝ 1/area (double the radius → area × 4 → resistance ÷ 4)
🌡️ Resistance and Temperature
For a metallic conductor, resistance increases linearly with temperature. When heated, atoms vibrate more, colliding more with electrons and impeding their flow.
🎯 Experiment: Variation of R with Temperature
Apparatus: coil of wire in glycerol, beaker, heat source, thermometer, ohmmeter.
Procedure: Heat slowly, read resistance from ohmmeter and temperature every 10°C.
Graph: R vs θ → straight line (not through origin)
Precaution: Use glycerol (not water) — better heat conduction and doesn't bubble around the coil.
Booklet II — Current Electricity
🌡️ Heating Effect & Joule's Law
Electric current heats wires. Joule discovered the exact relationship — and it explains why power lines use high voltage.
Three Effects of Electric Current
Heating Effect
Current heats wire. Used in toasters, kettles, electric heaters. Basis of Joule's Law.
Magnetic Effect
Current creates a magnetic field. Used in electromagnets, motors, loudspeakers.
Chemical Effect
Current drives chemical reactions. Used in electroplating, extracting metals from ores.
📖 Joule's Law
The rate at which heat is produced in a conductor is proportional to the square of the current, provided the resistance is constant.
⚠️ Joule's Law Formulas
P = I²R W = I²Rt
P = power/rate of heat production (W) I = current (A) R = resistance (Ω) t = time (s)
⚡ Why high voltage power lines? P = I²R means heat loss ∝ current². So if we transmit at higher voltage, we need less current (since P=VI stays the same). Less current → much less heat wasted. Transmitting at 300,000 V instead of 230 V reduces current by ~1300× and heat loss by ~1.7 million times!
🔌 Also Know: P = V²/R
By combining P=VI and V=IR, you can also show that P = V²/R. This is useful when given voltage and resistance but not current.
Booklet II — Current Electricity
🏠 Domestic Electric Circuits
How electricity is safely wired in your home — and how to answer those plug/fuse questions!
🔌 The 3-Pin Plug
Wire
Colour
Position in plug
Function
Live
Brown
Bottom Right
Carries current IN to appliance
Neutral
Blue
Bottom Left
Carries current OUT
Earth
Green/Yellow
Top
Safety — connected to metal casing
🧠 Memory trick: BRown = Bottom Right (Live), BLue = Bottom Left (Neutral). Earth = Top (it's the longest pin and connects first for safety!)
🔧 Safety Devices
Fuse
Wire that melts if current exceeds its rating. Always on the LIVE wire. Must replace after tripping.
MCB
Miniature Circuit Breaker. Trips automatically. Can be reset (unlike fuses). Contains electromagnet or bimetallic strip.
RCD
Residual Current Device. Detects difference between live and neutral currents. Faster and safer than MCB.
🔢 Choosing the Right Fuse
Calculate the expected current: I = P/V. Then choose the fuse with a rating just ABOVE the expected current.
🎯 Example: Kettle: P=2000W, V=230V. I = 2000/230 = 8.7 A. Choose the 13A fuse (next one above 8.7A). A 5A fuse would blow immediately!
💡 The Kilowatt-Hour
Your electricity bill is measured in kilowatt-hours (kWh). 1 kWh = energy used by a 1000W appliance in 1 hour.
kWh Calculation
kWh = kilowatts × hours
Cost = kWh × price per unit
Booklet II — Worked Examples
📐 Calculations: Booklet II
Circuits, resistivity, Joule's Law and power — all worked step by step.
Example 1 — Series & Parallel Circuit
Q: A 3Ω and 6Ω resistor in parallel, connected to a 1.5V supply. Find total resistance, total current, and current through 3Ω resistor.
Step 1: Parallel resistance
1/R = 1/3 + 1/6 = 3/6 → R = 2 Ω
Step 2: Total current
I = V/R = 1.5/2 = 0.75 A
Step 3: Current through 3Ω (V across parallel = 1.5V)
I₃ = V/R = 1.5/3 = 0.5 A
✅ R_total = 2Ω, I_total = 0.75A, I through 3Ω = 0.5A
r = 0.155mm = 0.155×10⁻³ m A = πr² = π(0.155×10⁻³)² = 7.55×10⁻⁸ m²
Use ρ = RA/L
ρ = (7.9)(7.55×10⁻⁸) / (0.546) = 1.09×10⁻⁶ Ω m
✅ Resistivity of nichrome = 1.09×10⁻⁶ Ω m
Example 3 — Joule's Law
Q: Aluminium wire, R=0.33Ω, carries current 250A for 10 min. Find heat energy produced.
W = I²Rt
t = 10 min = 600 s W = (250)²(0.33)(600) = 62500 × 0.33 × 600 = 1.238×10⁷ J
✅ Heat energy = 1.238×10⁷ J ≈ 12.4 MJ
Example 4 — Fuse Selection
Q: Vacuum cleaner: P=900W, V=230V. Which fuse? How many kWh in 90 minutes? Cost at 22c/unit?
Current: I = P/V
I = 900/230 = 3.9 A → use 5A fuse (next above 3.9)
kWh: P=0.9kW, t=1.5h
kWh = 0.9 × 1.5 = 1.35 kWh
Cost
Cost = 1.35 × 22 = 29.7 cent
✅ 5A fuse, 1.35 kWh, ≈30 cent
Booklet II — Quiz
✅ Quiz: Booklet II
Test yourself on Current, Resistance, Circuits, Joule's Law and Domestic Circuits!
Booklet III — Magnetism
🧲 Magnets & Magnetic Fields
Magnetism and electricity are deeply connected. Every electric current creates a magnetic field — and every changing magnetic field creates electricity!
📖 Magnetic Field
A magnetic field is any region of space where magnetic forces can be felt.
🧲 Basic Rules
Magnetic poles exist in pairs: North and South
Like poles REPEL, unlike poles ATTRACT
Magnetic field lines go from NORTH to SOUTH outside the magnet
Closer field lines = stronger field
⚡ Magnetic Field from a Current
Any wire carrying current creates a magnetic field around it. The direction depends on the current direction.
Straight Wire
Circular field lines around wire. Use Right Hand Grip Rule: grip wire with right hand, thumb points in direction of current, fingers curl in direction of field.
Solenoid (coil)
Magnetic field like a bar magnet. CIS Rule: Current going Clockwise = South pole facing you.
🔌 Electromagnets
A solenoid with a soft iron core = electromagnet. Advantages over permanent magnets:
Can be switched on and off
Strength can be varied (by changing current)
Applications: scrap yard cranes, electric bells, loudspeakers, relays
Booklet III — Magnetism
💡 Force on a Current in a Magnetic Field
Put a wire carrying current into a magnetic field and it experiences a force. This is the motor effect — and it's how every electric motor works!
⚠️ Force on a Current-Carrying Conductor
F = BIL
F = force on conductor (N) B = magnetic flux density (T, tesla) I = current in conductor (A) L = length of conductor in field (m)
🤚 Fleming's Left Hand Rule — Direction of Force
Point left hand fingers and thumb like "Stick 'em up!" (imagine you're a left-handed FBI agent):
Thumb (F)
Force direction
Index finger (B)
Field direction
Middle finger (I)
Current direction
🔵 Force on a Moving Charge
⚠️ Force on Moving Charge
F = Bqv (or F = Bev for electrons)
B = flux density (T) q = charge (C) v = velocity of charge (m s⁻¹)
🧠 Memory trick: The two formulas are "BIL and Bev" — think of them as people's names! Billy and Bev.
🔵 Circular Path in a Magnetic Field
A charged particle moving through a magnetic field at right angles to the field travels in a circle. Equate centripetal force = magnetic force:
Circular Path
Bqv = mv²/r → r = mv/(Bq)
Momentum: p = mv = Bqr
📏 Definition of the Ampere
📖 The Ampere
The ampere is the constant current which, flowing in two very long parallel wires one metre apart in a vacuum, produces a force of 2×10⁻⁷ N per metre length on each wire.
Booklet III — Electromagnetic Induction
⚡ Electromagnetic Induction
Faraday's greatest discovery: moving a magnet through a coil creates electricity. This is how nearly all the world's electricity is generated!
📖 Electromagnetic Induction
Electromagnetic induction occurs when an emf is induced in a coil due to a changing magnetic flux.
⚡ The Laws of Electromagnetic Induction
📖 Faraday's Law
The size of the induced emf is proportional to the rate of change of magnetic flux.
📖 Lenz's Law
The direction of the induced emf is always such as to oppose the change producing it.
⚠️ Magnetic Flux
Φ = BA
Φ = magnetic flux (Wb, weber) B = magnetic flux density (T) A = area perpendicular to field (m²)
⚠️ Induced EMF (Faraday's Law)
emf = N × (ΔΦ / Δt)
N = number of turns in coil ΔΦ = change in flux (Wb) Δt = time taken (s)
🧪 Demonstrating Lenz's Law — Copper Pipe
Drop a strong magnet through a copper pipe. It falls MUCH slower than through a plastic pipe! Why?
Falling magnet creates changing magnetic flux in copper pipe
Changing flux → induced emf → induced current (copper conducts)
This current creates a magnetic field opposing the motion (Lenz's Law)
The magnet is slowed down by this opposing field
Plastic pipe: no conductor → no current → no opposing field → normal speed
🔌 The Electric Generator
When a coil of wire rotates in a magnetic field (or a magnet rotates inside a coil), the flux through the coil changes continuously → emf induced → electricity produced! This is how nearly all power stations generate electricity.
⚡ Key point: A generator converts MECHANICAL energy to ELECTRICAL energy. An electric motor does the opposite — electrical to mechanical.
Booklet III — Electromagnetic Induction
🔄 Transformers & Alternating Current
Transformers change voltage using mutual induction. They're the reason electricity can be transmitted efficiently across the country.
📖 Alternating Current (AC)
Alternating current is current which continually changes direction. Mains electricity changes direction 50 times per second (50 Hz).
🔄 The Transformer
A transformer uses mutual induction: changing current in the primary coil creates a changing magnetic field in the iron core, which induces a changing emf in the secondary coil.
⚠️ Transformer Equation
Vs/Vp = Ns/Np
Vs = secondary voltage Vp = primary voltage Ns = turns in secondary Np = turns in primary
Step-up: Ns > Np → Vs > Vp Step-down: Ns < Np → Vs < Vp
🔌 Why high voltage transmission? Transformers allow us to step voltage up to ~300,000V for transmission. High V → low I → low I²R losses. Then step back down to 230V for homes.
📊 RMS Values for AC
AC voltage and current aren't constant — they vary sinusoidally. We use RMS (root mean square) values to compare AC to DC:
⚠️ RMS Values
V_rms = V_max / √2 I_rms = I_max / √2
An AC current with I_rms = 2A produces the same heating effect as 2A DC. Mains: V_max = 325V, so V_rms = 325/√2 ≈ 230V ✅
🔌 Self-Induction
When AC flows through a coil, the changing current creates a changing magnetic field in the coil itself, which induces an opposing emf (back-emf). This reduces the effective current. An inductor is a coil used to reduce AC current — like a dimmer switch on stage lights.
Booklet III — Worked Examples
📐 Calculations: Booklet III
Force on conductors, electromagnetic induction and transformer calculations — step by step.
Example 1 — Force on a Current-Carrying Conductor
Q: A conductor of length 50 cm carries 5A in a magnetic field of flux density 3T. Find the force.
F = BIL
F = (3)(5)(0.5) = 7.5 N
✅ Force = 7.5 N
Example 2 — Induced EMF (Faraday)
Q: A coil of 150 turns. Flux increases by 4.5×10⁻⁴ Wb in 3ms. Find the induced emf.
Vs = (Ns/Np) × Vp = (3000/150) × 12 = 20 × 12 = 240 V
✅ Output voltage = 240 V (step-up transformer)
Example 4 — RMS Voltage
Q: The peak voltage of an AC supply is 300V. Find the RMS voltage.
V_rms = V_max / √2
V_rms = 300 / √2 = 300 / 1.414 = 212 V
✅ V_rms = 212 V
Example 5 — Circular Path of Electron in Magnetic Field
Q: Electron (speed = 1.45×10⁸ m/s) in magnetic field B=90mT. Find radius. (m=9.1×10⁻³¹kg, e=1.6×10⁻¹⁹C)
Equate Bev = mv²/r → r = mv/(Be)
r = (9.1×10⁻³¹ × 1.45×10⁸) / (90×10⁻³ × 1.6×10⁻¹⁹) r = (1.32×10⁻²²) / (1.44×10⁻²⁰) r = 9.16×10⁻³ m ≈ 9.2 mm
✅ Radius = 9.16×10⁻³ m
Booklet III — Quiz
✅ Quiz: Booklet III
Test yourself on Magnetism, Electromagnetic Induction and Transformers!
📋 All Formulas — Quick Reference
Every formula you need for the Electricity Leaving Cert exam. Learn them!
Booklet I — Static & Capacitance
Coulomb's Law
F = Q₁Q₂/(4πεd²)
ε₀ = 8.9×10⁻¹² F m⁻¹ for air/vacuum
Electric Field Strength
E = F/Q E = Q/(4πεd²)
Work, Charge & Voltage
W = VQ
Capacitance
C = Q/V C = εA/d W = ½CV²
Booklet II — Current Electricity
Current & Charge
I = Q/t Q = It
Ohm's Law & Power
V = IR P = VI P = I²R P = V²/R
Resistors in Series/Parallel
Series: R_T = R₁+R₂ Parallel: 1/R_T = 1/R₁+1/R₂
Resistivity
R = ρL/A ρ = RA/L
A = πr² for a circular wire
Joule's Law
P = I²R W = I²Rt
Wheatstone Bridge (balanced)
R₁/R₂ = R₃/R₄
Booklet III — Magnetism & Induction
Force on Conductor & Charge
F = BIL F = Bqv
Magnetic Flux & Faraday's Law
Φ = BA emf = N(ΔΦ/Δt)
Transformer Equation
Vs/Vp = Ns/Np
RMS Values
V_rms = V_max/√2 I_rms = I_max/√2
Electron charge
1.6×10⁻¹⁹ C
ε₀
8.9×10⁻¹² F m⁻¹
Electron mass
9.1×10⁻³¹ kg
Mains voltage
230 V rms
📖 All Definitions — Learn These Off!
Word-for-word definitions. The key words are everything — miss one and lose marks!
Booklet I — Static & Capacitance
Coulomb's Law
The force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Electric Field
An electric field is a region of space where an electric charge experiences an electrostatic force.
Electric Field Strength (E)
Electric field strength at a point is the force per unit charge at that point. Unit: N C⁻¹.
Potential Difference
The potential difference between two points is the work done when a charge of 1 coulomb moves from one point to the other.
The Volt
The potential difference between two points is 1 volt if 1 joule of work is done when bringing a charge of 1 coulomb from one point to the other.
Capacitance
The capacitance of a conductor is the ratio of the charge on the conductor to its potential. C = Q/V. Unit: farad (F).
Relative Permittivity (εᵣ)
Relative permittivity is defined as the ratio of the permittivity of a medium to the permittivity of a vacuum. It has no unit.
Booklet II — Current Electricity
Electric Current
Electric current is a measure of the rate of flow of charge. I = Q/t. Unit: ampere (A).
The Coulomb
The coulomb is the amount of charge that passes when a current of one ampere flows for one second.
Resistance
The resistance of a conductor is the ratio of the potential difference across it to the current flowing through it. Unit: ohm (Ω).
Ohm's Law
The current flowing through a conductor is directly proportional to the potential difference across it, assuming constant temperature.
Resistivity
Resistivity is defined as the resistance of a cube of material of side one metre. Unit: Ω m.
Joule's Law
The rate at which heat is produced in a conductor is proportional to the square of the current, provided the resistance is constant. P = I²R.
Booklet III — Magnetism & Induction
Magnetic Field
A magnetic field is any region of space where magnetic forces can be felt.
Magnetic Flux (Φ)
Magnetic flux is defined as the product of magnetic flux density and the area (perpendicular to the flux). Φ = BA. Unit: weber (Wb).
Electromagnetic Induction
Electromagnetic induction occurs when an emf is induced in a coil due to a changing magnetic flux.
Faraday's Law
The size of the induced emf is proportional to the rate of change of magnetic flux.
Lenz's Law
The direction of the induced emf is always such as to oppose the change producing it.
The Ampere
The ampere is the constant current which, flowing in two very long parallel wires one metre apart in a vacuum, produces a force of 2×10⁻⁷ N per metre length on each wire.
Alternating Current
Alternating current is current which continually changes direction.
🎯 Exam tip: The words in bold are essential — "rate of flow", "per unit charge", "proportional to the square of", "oppose the change". Missing key phrases costs marks. Learn definitions exactly!