Electric charge (symbol: q or Q) is a fundamental property of matter that causes it to experience a force near other charged matter. Two types: positive (+) and negative (−).
Think of charge as a "tag" on particles. Protons carry +, electrons carry −, neutrons are neutral (no tag).
The Golden Rule
+
⟵ REPEL ⟶
+
−
⟵ REPEL ⟶
−
+
⟶ ATTRACT ⟵
−
"Opposites attract, likes repel." This shows up on EVERY test.
Rubber is an insulator → blocks electron flow → prevents electric shock.
5. Static Electricity — Charges at Rest
Definition
Static electricity = buildup of electric charge on an object's surface. Unlike current electricity (flowing electrons), static charges stay put until they find a path to discharge.
Touching a charged object to a neutral one shares charge directly.
📌 Charged rod touches metal sphere → both share charge.
③ Induction (No Contact!)
A charged object near a conductor rearranges charges inside without touching.
📌 Negative rod near metal sphere → electrons repelled to far side → near side (+), far side (−). Ground the far side → electrons escape to ground → remove rod → sphere is permanently (+)!
Induction: charge an object without ever touching it
Sources & Hazards of Static
Sources: Friction (walking on carpet, clothes dryer), separation of materials, flowing liquids/gases
⚡ Sparks: Can ignite flammable vapors, dusts, or gases (gas station danger!)
💻 ESD: Electrostatic discharge destroys sensitive electronics like computer chips
⚡ Lightning: Massive static discharge between clouds and ground
The #1 tested static hazard: "sparks that can ignite flammable vapors." That's why gas stations have grounding straps and "touch metal before refueling" signs.
6. Electric Fields — The Invisible Force Zone
Definition
An electric field (E) is the region around a charged object where other charges experience a force. Every charge creates a field extending into space.
Field Line Rules (Important!)
Lines point away from (+) charges and toward (−) charges
More lines = stronger field
Lines never cross
Lines are closer together where the field is stronger
Electric field lines: outward from positive, inward toward negative
Electric Field Formula
E = F / q
E = electric field strength (N/C or V/m)F = force on the test charge (Newtons)q = test charge (Coulombs)
You can also calculate the field from a single point charge:
E = ke × Q / r²
ke = 8.99 × 10⁹ N·m²/C² (Coulomb's constant)Q = source charge creating the fieldr = distance from the charge
Example
Q: A +2 μC charge creates an electric field. What is E at a point 0.5 m away?
E = k × Q / r² = (8.99 × 10⁹)(2 × 10⁻⁶) / (0.5)²
E = (8.99 × 10⁹)(2 × 10⁻⁶) / 0.25 = 17,980 / 0.25 = 71,920 N/C
Direction: away from the positive charge.
Think of it like gravity: A planet creates a gravitational field around it. Similarly, a charge creates an electric field around it. Other charges placed in that field feel a force — just like objects near a planet feel gravitational pull!
7. Coulomb's Law — The Math of Electric Force
The Big Formula
This is one of the most important equations for Circuit Lab. It tells you the force between two charged objects.
F = ke × |q₁| × |q₂| / r²
F = electrostatic force between the charges (Newtons, N)ke = Coulomb's constant = 8.99 × 10⁹ N·m²/C²q₁, q₂ = the two charges (Coulombs, C)r = distance between the centers of the charges (meters, m)
What Coulomb's Law Tells Us
Directly Proportional to Charges
Double one charge → force doubles. Double both charges → force quadruples (4×).
Inversely Proportional to Distance²
Double the distance → force drops to 1/4. Triple the distance → force drops to 1/9. This is called an inverse-square law.
Worked Example 1
Q: Two charges, q₁ = +3 μC and q₂ = −5 μC, are 0.2 m apart. What is the force?
Given: q₁ = 3 × 10⁻⁶ C, q₂ = 5 × 10⁻⁶ C, r = 0.2 m
F = k × |q₁| × |q₂| / r²
F = (8.99 × 10⁹)(3 × 10⁻⁶)(5 × 10⁻⁶) / (0.2)²
F = (8.99 × 10⁹)(15 × 10⁻¹²) / 0.04
F = 0.13485 / 0.04 = 3.37 N Direction: Attractive (opposite charges → they pull toward each other).
Worked Example 2 — Distance Change
Q: Two charges have a force of 12 N between them. If you double the distance, what's the new force?
Inverse square law: F ∝ 1/r²
Double distance → r becomes 2r → r² becomes 4r²
New force = 12 / 4 = 3 N
The forcedrops to one-quarter!
Worked Example 3 — Charge Change
Q: Two charges produce a force of 8 N. If you triple one of the charges, what happens to the force?
F ∝ q₁ × q₂ (directly proportional)
Triple one charge → force triples → 24 N
Watch out for the r² in the denominator! Students often forget to square the distance. If r = 0.3 m, you use 0.09, not 0.3.
Coulomb's Law looks just like Newton's Law of Gravity!
Gravity: F = G × m₁m₂/r² (masses attract)
Coulomb: F = k × q₁q₂/r² (charges attract OR repel)
Same shape, but gravity only attracts. Electric force can attract or repel!
8. Capacitance — Storing Charge
Definition
Capacitance is the ability to store electric charge. A capacitor is a device built specifically to do this — two metal plates separated by an insulating material (dielectric).
C = Q / V
C = capacitance (Farads, F)Q = charge stored (Coulombs, C)V = voltage across the capacitor (Volts, V)
1 Farad is HUGE — it means storing 1 coulomb for every volt. Real capacitors are usually measured in:
Prefix
Symbol
Value
Common Use
Microfarad
μF
10⁻⁶ F
Power supplies, audio circuits
Nanofarad
nF
10⁻⁹ F
Signal filtering
Picofarad
pF
10⁻¹² F
Radio, high-frequency circuits
How a Capacitor Works
Two metal plates separated by an insulator. Charge builds up on the plates.
What Affects Capacitance?
Larger plate area → more capacitance (more room for charge)
Smaller plate gap → more capacitance (stronger electric field)
Better dielectric → more capacitance (insulator quality matters)
Worked Example
Q: A 100 μF capacitor is connected to a 9V battery. How much charge does it store?
C = Q / V → Q = C × V Q = (100 × 10⁻⁶)(9) = 900 μC = 0.0009 C
Worked Example
Q: A capacitor stores 0.005 C at 25V. What is its capacitance?
C = Q / V = 0.005 / 25 = 0.0002 F = 200 μF
Polarized vs. Non-Polarized Capacitors
Polarized (Electrolytic)
Has a + and − side. Must be connected correctly or it can be damaged/explode!
Examples: aluminum electrolytic, tantalum. Typical values: larger (1 μF to thousands of μF)
Non-Polarized (Ceramic/Film)
Can be connected either way — no polarity.
Examples: ceramic disc, film capacitors. Typical values: smaller (pF to low μF)
On the test, if they show a capacitor with a + marking, it's polarized. Connecting it backward can destroy it!
Think of a capacitor like a tiny rechargeable battery — but one that charges and discharges in fractions of a second. It stores energy temporarily, not long-term.
Massive charge buildup in clouds discharges to ground
Lightning rods (conductors that safely direct current to ground)
Surgical/hospital risks
Sparks near flammable anesthetic gases
Conductive shoes, grounded equipment
Key Takeaway
The common thread: static discharge (sparks) + flammable material = danger. Prevention always involves grounding — giving charge a safe path to flow away.
10. Key Person: Charles-Augustin de Coulomb
Historical Figure
Charles-Augustin de Coulomb (1736–1806) was a French physicist who discovered the law governing the force between electric charges.
Nationality: French
Era: 18th century
Famous for: Coulomb's Law — the inverse-square law of electrostatic force
Tool: Invented the torsion balance to precisely measure tiny forces between charged objects
Unit named after him: The coulomb (C) — the SI unit of electric charge
Key insight: Showed that electric force follows the same mathematical pattern as Newton's gravitational force (inverse-square law)
The test will ask which scientist is associated with the force between charges or the unit of charge. Answer: Coulomb. Don't confuse with Ampere (current), Ohm (resistance), or Volta (voltage).
11. Practice Problems (15 Questions)
Select an answer or type your response, then click Submit to check yourself.
Q1
Which of the following best describes Coulomb's Law?
Q2
Which unit measures electric charge?
Q3
Which of the following best represents a hazard of static electricity?
Q4
An object has 5 more protons than electrons. What is its charge?
Q5
Two charges of +4 μC and −6 μC are 0.3 m apart. Calculate the force between them.
Q6
Two charges exert a force of 20 N on each other. If the distance between them is tripled, what is the new force?
Q7
Define capacitance and give its SI unit.
Q8
A rubber rod is rubbed with fur. The rod becomes negatively charged. Explain what happened using conservation of charge.
Q9
Electric field lines around a positive charge point:
Q10
A 220 μF capacitor is connected to a 12V battery. How much charge is stored?
Q11
Is a charge of 6.408 × 10⁻¹⁹ C possible? Why or why not?
Q12
Which of the following is a conductor?
Q13
Two identical metal spheres have charges of +8 μC and −2 μC. They are touched together and then separated. What is the charge on each sphere?
Q14
Two charges produce a force of 10 N. If one charge is doubled AND the distance is halved, what is the new force?
Q15
A capacitor stores 500 μC of charge when connected to a 10V source. What is its capacitance? If the voltage is increased to 20V, how much charge will it store?
12. 📝 Cheat Sheet — Topic 1
Concept
Key Facts
Electric Charge
Property of matter. Two types: + and −. Like repels, opposite attracts. Unit: Coulomb (C).
Elementary Charge
e = 1.602 × 10⁻¹⁹ C. Proton = +e, electron = −e.
Quantization
q = n × e (charge is always a whole number of electrons).
Conservation
Charge cannot be created or destroyed — only transferred.
Conductors
Metals. Electrons flow freely. Low resistance.
Insulators
Non-metals (rubber, glass, plastic). Block electron flow.
Static Electricity
Charge buildup. Three methods: friction, conduction, induction.
Static Hazards
#1: Sparks igniting flammable vapors. Also ESD on electronics.
Electric Field
E = F/q = k×Q/r². Lines: away from (+), toward (−). Unit: N/C or V/m.
Coulomb's Law
F = k|q₁||q₂|/r². k = 8.99 × 10⁹. Inverse-square law.
Capacitance
C = Q/V. Unit: Farad (F). μF, nF, pF for smaller values.
Coulomb (person)
French physicist (1736–1806). Torsion balance. Inverse-square law for charge.
Formula Quick Reference:
F = k|q₁||q₂|/r² (force between charges)
E = F/q = kQ/r² (electric field)
C = Q/V (capacitance)
k = 8.99 × 10⁹ N·m²/C² | e = 1.602 × 10⁻¹⁹ C
1. What Is Direct Current (DC)?
Key Definition
Direct Current (DC) is electric current that flows in one direction only. Electrons always move from the negative terminal, through the circuit, and back to the positive terminal.
Think of DC like a river — water flows steadily in one direction. The current never reverses.
Characteristics of DC
Direction: Always one way (unidirectional)
Voltage: Constant (steady) — doesn't oscillate
Frequency: 0 Hz (no oscillation)
Graph shape: A flat horizontal line on a voltage-vs-time graph
DC voltage stays flat — constant and steady, unlike AC which oscillates
"DC = Direct = one Direction, Constant." Just remember: DC is the simple one. One way, steady flow.
2. DC vs. AC — Quick Comparison
Why This Matters
DC and AC are the two fundamental types of electric current. This topic focuses on DC, but know the difference!
Property
DC (Direct Current)
AC (Alternating Current)
Direction
One way only
Reverses back and forth
Voltage
Constant
Oscillates (sine wave)
Frequency
0 Hz
60 Hz (US) / 50 Hz (world)
Source
Batteries, solar cells
Power plants, wall outlets
Travel distance
Short (loses energy)
Long (transformers help)
Symbol
— (straight line)
~ (wavy line)
The test loves: "Name a DC device" → flashlight, phone, laptop. "Name an AC device" → wall outlet, toaster, refrigerator.
3. DC Sources — Batteries & Beyond
Key Concept
A DC source provides a steady voltage that pushes electrons in one direction. The most common DC source is a battery.
Source
How It Works
Example
Battery (cell)
Chemical energy → electrical energy
AA, AAA, 9V, car battery
Solar cell
Sunlight knocks electrons loose in semiconductor
Roof panels, calculators
DC power supply
Converts AC from wall → DC (rectifier)
Phone charger, laptop adapter
DC generator
Spinning coil in magnetic field + commutator
Old-style generators
💡 Real World
Your phone charger takes AC from the wall (120V, 60Hz in the US) and converts it to DC (usually 5V). That brick on the cable is a rectifier!
A battery does NOT "store electricity." It stores chemical energy and converts it to electrical energy through chemical reactions.
4. Inside a Battery — How It Works
Key Components
A battery has three essential parts: an anode (negative electrode), a cathode (positive electrode), and an electrolyte (chemical medium).
Chemical reactions at the anode release electrons; they travel through the circuit to the cathode
How It Works
Anode (−): Chemical reaction oxidizes → releases electrons
Electrons flow through the external circuit (this is your current!)
Cathode (+): Chemical reaction reduces → absorbs electrons
Electrolyte: Carries ions between electrodes inside to complete the circuit
When the chemicals are used up → battery is "dead"
Cell vs. Battery
A cell = single electrochemical unit (one AA). A battery = two or more cells connected (a 9V = six 1.5V cells in series). Everyday language uses "battery" for both.
"An Ox, Red Cat" — Anode = Oxidation, Reduction = Cathode. Works in chemistry AND physics!
5. Battery Configurations: Series & Parallel
Key Concept
Connect multiple batteries together to change total voltage or capacity. Series = voltages add. Parallel = capacity adds.
Batteries in Series
Connect + to − in a chain. Voltages add up. Current capacity stays the same.
Vtotal = V₁ + V₂ + V₃ + ...
Series: connect (+) to (−) of the next battery. Voltage adds, capacity stays the same.
Batteries in Parallel
Connect all (+) together and all (−) together. Voltage stays the same, capacity multiplies.
Vtotal = V (same as one battery)
Parallel: voltage unchanged, but the batteries last longer (capacity adds).
Science Olympiad often asks: "How do you increase voltage?" → Series. "How do you increase battery life?" → Parallel.
Never connect batteries of different voltages in parallel! The higher-voltage battery will force current backward through the weaker one, causing overheating or damage.
6. Internal Resistance
Key Concept
Every real battery has some resistance inside it called internal resistance (r). It wastes a bit of voltage as heat inside the battery, so the voltage you actually get is less than the rated voltage.
Vterminal = EMF − I × r
Vterminal = voltage actually delivered to the circuit (V)EMF (ε) = electromotive force — the battery's "ideal" voltage (V)I = current flowing (A)r = internal resistance (Ω)
Worked Example
Q: A 9V battery has an internal resistance of 0.5 Ω. If 2A of current flows, what is the terminal voltage?
Vterminal = EMF − Ir = 9 − (2)(0.5) = 9 − 1 = 8V
The battery "loses" 1V as heat internally, delivering only 8V to the circuit.
Worked Example 2 — Finding Internal Resistance
Q: A battery's EMF is 12V. When a 4A current flows, the terminal voltage drops to 10V. What is the internal resistance?
Vterminal = EMF − Ir
10 = 12 − 4r → 4r = 2 → r = 0.5 Ω
Old batteries have higher internal resistance! That's why a "dead" battery still shows ~1.3V on a meter but can't power your flashlight — too much voltage is dropped internally when current flows.
If a test shows a battery with EMF and internal resistance, always use V = EMF − Ir for the actual circuit voltage, not the rated EMF.
7. DC Circuit Components
A DC circuit is made of components connected by wires. Know each component's job!
🔗 Wires
Conductors (usually copper) that carry current between components. Ideal wires have zero resistance. In reality, very low resistance.
🔲 Resistors
Oppose current flow. Measured in Ohms (Ω). Convert electrical energy to heat. Used to control current and voltage in circuits.
🔘 Switches
Open or close a circuit. Closed switch = current flows. Open switch = circuit broken, no current. Like a door for electrons.
💡 Bulbs (Incandescent)
Resistors that produce light and heat. The filament has resistance. Brightness depends on power (P = I²R). More current → brighter light.
💡 LEDs (Light-Emitting Diodes)
Emit light when current flows in the correct direction only. More efficient than bulbs. Require a current-limiting resistor to prevent burnout. Have a minimum forward voltage (~1.8–3.3V).
⚡ Fuses
Safety devices. A thin wire that melts and breaks if current exceeds a safe limit. One-time use — must be replaced. Protects the circuit from overcurrent damage.
Component
Symbol Description
Key Property
Battery/Cell
Long line (+) and short line (−)
Provides EMF (voltage)
Resistor
Rectangle or zigzag
Resistance in Ω
Switch (open)
Gap in wire with lever
Breaks circuit
Switch (closed)
Lever touching contact
Completes circuit
Bulb/Lamp
Circle with X or filament
Light + heat output
LED
Triangle with arrow pointing to line
Light, one direction only
Fuse
Rectangle with line through it
Current limit protection
Capacitor
Two parallel lines
Stores charge (Farads)
For Science Olympiad: know whether each component is in series (one path) or can be in parallel (multiple paths). Fuses are always in series — to protect the whole circuit.
8. Circuit Diagrams & Schematic Symbols
Why Schematics Matter
A schematic diagram uses standardized symbols to represent circuits. Every engineer and physicist uses the same symbols worldwide. Reading schematics is a core Science Olympiad skill!
Memorize these symbols — every schematic question uses them!
Key rule: A dot (•) where wires cross means they ARE connected. No dot means they just cross without connecting. This trips up many students!
How to Read a Schematic
Identify the power source (battery)
Trace the path(s) electrons can take
Identify each component and its value
Determine if components are in series (one path) or parallel (multiple paths)
Apply Ohm's Law and Kirchhoff's laws
9. Series Circuits
Key Definition
In a series circuit, components are connected end-to-end in a single loop. There is only one path for current to flow.
Series circuit: one loop, same current through all components
Rules for Series Circuits
Current — Same Everywhere
Itotal = I₁ = I₂ = I₃ Current has only one path, so the same current flows through every component.
Voltage — Divides Up
Vtotal = V₁ + V₂ + V₃ Each resistor "uses up" part of the total voltage. They add back to the source voltage.
Resistance — Adds Directly
Rtotal = R₁ + R₂ + R₃ + ... More resistors in series = more total resistance.
If One Component Fails...
The circuit breaks completely. Like old Christmas lights — if one bulb goes out, they all go out. No alternative path!
Worked Example
Q: Three resistors R₁ = 10Ω, R₂ = 20Ω, R₃ = 30Ω are in series with a 12V battery. Find total resistance, current, and voltage across each resistor.
Students often try to ADD resistances in parallel — wrong! Use the reciprocal formula. Rtotal gets SMALLER when you add parallel resistors.
Special case — Two equal resistors in parallel: Rtotal = R/2. Three equal resistors: R/3. This shortcut saves time on timed tests!
11. Series vs. Parallel — Side by Side
Property
Series
Parallel
Number of paths
One path only
Multiple paths
Current
Same through all: I₁=I₂=I₃
Splits: Itotal=I₁+I₂+I₃
Voltage
Divides: Vtotal=V₁+V₂+V₃
Same across all: V₁=V₂=V₃
Resistance formula
Rtotal = R₁+R₂+R₃ (increases)
1/Rtotal=1/R₁+1/R₂+1/R₃ (decreases)
Effect of adding more
R increases, current decreases
R decreases, current increases
One component fails
All stop (circuit broken)
Others keep working
Bulb brightness
Dimmer (share voltage)
Same brightness (each gets full V)
Real-world use
Old string lights, simple switches
House wiring, modern lights
Bulb Brightness in Series vs. Parallel
Series — Dimmer Bulbs
Two 100Ω bulbs in series with 12V: I = 12/(100+100) = 0.06A Power per bulb: P = I²R = (0.06)² × 100 = 0.36W Bulbs are dim — they share the voltage.
Parallel — Same Brightness
Two 100Ω bulbs in parallel with 12V: Each sees full 12V. I = 12/100 = 0.12A each. Power per bulb: P = V²/R = 144/100 = 1.44W Bulbs are bright — each gets full voltage.
Key exam question: "If you add another bulb in parallel, what happens to the others?" → They stay the same brightness (same voltage, same power). "If you add another bulb in series?" → They all get dimmer (voltage divides further).
12. Ohm's Law & Power
The Most Important Formula in DC Circuits
Ohm's Law: V = I × R | I = V/R | R = V/I
V = I × R
V = Voltage (Volts, V) — the "push" driving currentI = Current (Amperes, A) — the rate of electron flowR = Resistance (Ohms, Ω) — opposition to current flow
The Ohm's Law Triangle
Cover V → I×R. Cover I → V/R. Cover R → V/I.
Power Formulas
Power (P) measures how fast electrical energy is converted. Unit: Watts (W).
P = I × V = I²R = V²/R
P = Power in Watts (W)P = IV — use when you know current and voltageP = I²R — use when you know current and resistanceP = V²/R — use when you know voltage and resistance
All the Ohm/Power Formulas
From V=IR and P=IV, you can derive 12 combinations:
V = IR = P/I = √(PR)
I = V/R = P/V = √(P/R)
R = V/I = V²/P = P/I²
P = IV = I²R = V²/R
Energy vs. Power
Power = energy per second (Watts) Energy = Power × Time
E = P × t (Joules when P in W, t in seconds)
Don't confuse voltage and power! A 60W bulb and a 100W bulb connected to the same 120V outlet: the 100W bulb draws more current (I = P/V = 0.83A vs 0.5A) and is brighter.
13. DC Hazards & Safety
Why It Matters
DC electricity can be dangerous. Understanding hazards keeps you and circuits safe — and it's tested on Science Olympiad!
Electric Shock
Current through the human body is what kills — not voltage alone. As little as 100 mA (0.1A) through the heart can be fatal.
Current
Effect on Human Body
1–5 mA
Tingling, slight shock
10–20 mA
Painful shock, cannot let go
50–100 mA
Severe shock, heart risk
100–200 mA
Ventricular fibrillation — potentially fatal
Over 1A
Severe burns, cardiac arrest
Short Circuits
What Is a Short Circuit?
A direct connection between + and − with very low resistance. Current follows an unintended low-resistance path.
Using R = V/I: if R ≈ 0, then I → huge → wires overheat → fire!
Prevention
Fuses — melt to break the circuit
Circuit breakers — reset automatically
Proper insulation on all wires
Don't connect battery terminals directly!
Overheating & Thermal Runaway
Components dissipate power as heat (P = I²R). If current is too high or ventilation is poor, components can overheat, melt insulation, or ignite nearby materials. Always check current ratings!
Battery Hazards
Reverse polarity: Connecting a battery backward can destroy polarized components (electrolytic capacitors, LEDs) — and cause explosions!
Overcharging: Can cause lithium batteries to swell, leak, or catch fire (thermal runaway)
Short circuit: A shorted battery can heat dangerously fast — never put loose batteries in a bag with metal objects
Chemical leakage: Old alkaline batteries can leak corrosive electrolyte
Common Science Olympiad hazard question: "What protects a circuit from overcurrent?" → Fuse or circuit breaker. "What component should never be reverse-connected?" → Polarized capacitor, LED, diode.
Safety Rules for DC Circuits
Always disconnect power before modifying a circuit
Use properly rated fuses/breakers for expected currents
Check polarity before connecting polarized components
Never exceed voltage/current ratings of components
Keep flammable materials away from circuits
Use anti-static precautions near sensitive electronics
14. Real-World DC Applications
Application
DC Component
Why DC?
Smartphones/tablets
Li-ion battery, 3.7V typical
Portable, rechargeable, consistent voltage
Laptops
Li-ion battery, 11–20V
Needs stable DC; AC adapter converts from outlet
Electric vehicles (EVs)
Large Li-ion pack (300–800V DC)
Motors can run on DC; fast charging = DC
LED lighting
LED strips, 12V DC
LEDs require DC; efficient, long-lasting
Solar panels
Photovoltaic cells, 12–48V
Cells produce DC directly from sunlight
Flashlights
AA/AAA batteries, 1.5V×cells
Simple, portable DC source
Remote controls
AAA or coin cell, 1.5–3V
Low-power electronics need stable DC
Computer motherboards
ATX supply: 3.3V, 5V, 12V DC
CPUs and RAM require precise DC voltages
DC in Modern Technology
🔋 The Battery Revolution
Li-ion batteries transformed portable electronics. Laptops, phones, EVs all depend on DC power. Tesla's Model S uses ~7,000 cylindrical Li-ion cells!
☀️ Solar Energy
Solar panels produce DC. Inverters convert DC → AC for home use, or batteries store DC directly. The world is gradually shifting toward DC microgrids for efficiency.
💡 Fun Fact
When you plug in your phone charger, it converts 120V AC (from the outlet) to ~5V DC. The "brick" is called a switched-mode power supply (SMPS). Without it, your phone would explode in milliseconds!
15. Key Person: Alessandro Volta
Historical Figure
Alessandro Volta (1745–1827) was an Italian physicist who invented the first true battery — the voltaic pile — in 1800.
Nationality: Italian
Era: 18th–19th century
Famous for: Inventing the first electrochemical battery (voltaic pile, 1800)
The voltaic pile: Alternating zinc and copper discs separated by saltwater-soaked cloth — stacked to produce a sustained electrical current
Unit named after him: The volt (V) — the SI unit of electric potential difference
Influenced by: Luigi Galvani's experiments with frog legs (animal electricity)
Impact: First device to produce a steady, continuous electrical current — launched the age of electrical science
Science Olympiad loves: "Who invented the battery?" → Volta. "What is voltage named after?" → Volta. Don't confuse with Ampere (current) or Ohm (resistance)!
Remember: Volt → Volta → Voltage. The unit is named after the person who made sustained voltage possible!
16. Practice Problems (15 Questions)
Select an answer or type your response, then click Submit to check yourself.
Q1
Three resistors of 10Ω, 15Ω, and 25Ω are connected in series to a 25V battery. What is the total resistance and current?
Q2
Two resistors of 12Ω and 6Ω are connected in parallel. What is their combined resistance?
Q3
A battery has an EMF of 6V and internal resistance of 0.2Ω. If 3A of current flows, what is the terminal voltage delivered to the circuit?
Q4
Which statement about parallel circuits is correct?
Q5
A 40Ω resistor carries 0.3A of current. What is the voltage across it, and how much power does it dissipate?
Q6
Two identical 60W bulbs are connected in parallel across 120V. What is the total current drawn from the source?
Q7
In a series circuit with a 24V battery, three equal resistors each have a voltage of 8V across them. What is the resistance of each if the current is 0.4A?
Q8
What type of energy does a battery store, and how does it produce electrical energy?
Q9
Three 30Ω resistors are connected in parallel. What is the combined resistance?
Q10
You have a circuit with a 9V battery, a 27Ω resistor, and an LED in series. The LED has a forward voltage of 2V. What current flows through the LED, and what is its power consumption?
Q11
A 100W light bulb runs for 8 hours every day for 30 days. How many kilowatt-hours of energy does it use?
Q12
What happens to the other bulbs in a series string when one bulb burns out? Why? What about in a parallel circuit?
Q13
Which scientist invented the first battery, and what is the unit of voltage named after them?
Q14
A fuse rated at 5A is placed in a circuit. The circuit has a 12V battery and three 2Ω resistors in series. Will the fuse blow?
Q15
In a parallel circuit, resistors of 4Ω, 6Ω, and 12Ω are connected to a 12V battery. Find: (a) total resistance, (b) total current, (c) current through each branch.
17. 📝 Cheat Sheet — Topic 2: DC Circuits
Concept
Key Facts
DC (Direct Current)
One direction only. Constant voltage. 0 Hz. From batteries.
Battery
Chemical → electrical energy. Anode (−) oxidizes, cathode (+) reduces. Cell vs. battery.
Series Batteries
Vtotal = V₁+V₂+... (voltages add)
Parallel Batteries
Voltage unchanged, capacity (life) adds
Internal Resistance
Vterminal = EMF − Ir
Ohm's Law
V = IR | I = V/R | R = V/I
Series Circuits
Rtotal=ΣR. Same I. V divides. One fails → all fail.
Parallel Circuits
1/Rtotal=Σ(1/R). Same V. I divides. One fails → others work.
Power
P = IV = I²R = V²/R (Watts)
Energy
E = Pt (Joules) or kWh
Fuse
Protects against overcurrent. Always in series. One-time use.
LED
Light from current (one direction). Needs current-limiting resistor.
Volta (person)
Italian physicist (1745–1827). Invented voltaic pile (first battery). Volt named after him.
Formula Quick Reference — DC Circuits:
V = IR | Rseries = R₁+R₂+... | 1/Rparallel = 1/R₁+1/R₂+...
P = IV = I²R = V²/R | Vterminal = EMF − Ir
Series: same I, V divides | Parallel: same V, I divides