Electricity Formula CheatSheet

A complete, intuitive guide for students, electricians, and curious learners

⚡ 1. Ohm’s Law

$$V=I\times R$$

Voltage is the push, current is the flow, resistance is the opposition.

What it means

If you increase the push (voltage), more current flows — unless resistance blocks it.

Analogy

Imagine water flowing through a pipe:

• Voltage = water pressure

• Current = water flow

• Resistance = narrowness of the pipe

Narrow pipe → less water flows even if pressure is high.

Explore more: Ohm’s Law

⚡ 2. Current Formula

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

Current increases when voltage increases or resistance decreases.

Analogy

More pressure or a wider pipe → more water flow.

Explore: Electric Current

⚡ 3. Resistance Formula

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

Resistance tells how much a material slows down current.

Analogy

If you know water pressure and flow, you can calculate how narrow the pipe is.

Explore: Resistance

⚡ 4. Power Formulas

$$P=V\times I,P=I^{2}R,P=\frac{V^2}{R}$$

Power is the rate of electrical work — how fast energy is used.

Analogy

Power is like how fast a car burns fuel. Higher voltage or current → more “fuel burn.”

Explore: Electrical Power

⚡ 5. Energy Formula

$$E=P\times t$$

Energy is total work done over time.

Analogy

If power is “speed of fuel burn,” energy is “total fuel burned.”

Explore: Electrical Energy

⚡ 6. AC Power (Single Phase)

$$P=V\times I\times \cos \theta$$

The term cosθ is the power factor, showing how efficiently power is used.

Analogy

Imagine pushing a box:

• If you push straight → full power

• If you push at an angle → some effort is wasted

Power factor tells how much effort is actually useful.

Explore: Power Factor

⚡ 7. AC Power (Three Phase)

$$P=\sqrt{3}\times V\times I\times \cos \theta$$

Three‑phase systems deliver more power smoothly.

Analogy

Three people pushing a cart from different angles → smoother, stronger push.

Explore: Three Phase Power

⚡ 8. Frequency

$$f=\frac{1}{T}$$

Frequency is how many cycles occur per second.

Analogy

If a fan completes 60 rotations per second → frequency = 60 Hz.

Explore: Frequency

⚡ 9. Capacitance

$$Q=C\times V$$

Capacitance tells how much charge a capacitor can store at a given voltage.

Analogy

A capacitor is like a water tank:

• Bigger tank (higher C) → stores more water (charge) at same pressure (voltage).

Explore: Capacitance

⚡ 10. Inductive Reactance

$$X_L=2\pi fL$$

Inductors resist changes in current. Higher frequency → higher reactance.

Analogy

An inductor is like a heavy door:

• Slow push → easy

• Fast push → door resists more

Explore: Inductive Reactance

⚡ 11. Capacitive Reactance

$$X_C=\frac{1}{2\pi fC}$$

Capacitors resist changes in voltage. Higher frequency → lower reactance.

Analogy

A capacitor is like a spring:

• Slow push → spring resists

• Fast push → spring moves easily

Explore: Capacitive Reactance

⚡ 12. Impedance

$$Z=\sqrt{R^2+X^2}$$

Impedance is the total opposition in AC circuits — combining resistance and reactance.

Analogy

Imagine walking through a forest:

• Resistance = straight path obstacles

• Reactance = obstacles that appear only when you move fast Impedance = total difficulty of the journey.

Explore: Impedance

🌟 Conclusion — Why This Cheat Sheet Matters

These formulas are the foundation of electrical engineering. They help you understand:

• How circuits behave

• How appliances consume energy

• How AC systems work

• How power is calculated

• How real‑world electrical systems are designed

With analogies, each formula becomes intuitive, not just mathematical.

If you want, I can turn this blog into a chapter‑style PDF, or expand it with diagrams for each formula.

Electricity Carton

 Neeraj — I’ve got you. Here is your complete NEW storybook‑style comic, fully updated with:

• Joule‑visualization scenes

• The new “Why V = IR?” scene with Volt, Amp, and Ohm

• All previous electricity + force + work content

• Clean, continuous flow

• Big illustrated panels (via image tags)

• A full worksheet at the end

This is now the definitive comic version of your science story.

🎉 THE COMPLETE STORYBOOK COMIC

“The Adventures of Volt, Amp, Ohm, Forcey, Theta, Joule & Chargey!”

(Fully Updated Edition)

⭐ PAGE 1 — Meet Chargey

Chargey: “I’m tiny, but when many of us move together, we create electricity!”

⭐ PAGE 2 — Volt Arrives

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Volt: “I give energy to each Coulomb of charge. If I’m 1 Volt, each Coulomb gets 1 Joule!”

Chargey: “So you give energy per charge?”

Volt: “Exactly! That’s why Voltage means energy per Coulomb.”

⭐ PAGE 3 — Joule Appears (NEW SCENE)

A glowing character appears holding tiny golden packets.

Joule: “I’m the packet of energy Volt gives you!”

Chargey: “What does 1 Joule look like?”

Joule: “Let me show you!”

⭐ PAGE 4 — Joule Shows Real‑World Examples

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Joule: “These everyday actions each use about 1 Joule of energy!”

• Lifting an apple 10 cm

• Pushing a toy car gently

• Flicking a marble

• A tiny hop

⭐ PAGE 5 — Connecting Joules to Voltage

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Volt hands Chargey glowing packets.

Volt: “If I’m 1 Volt, I give 1 Joule to each Coulomb.”

Chargey: “So if you’re 9 Volts, I get 9 Joules?”

Volt: “Yes! More voltage → more energy packets per Coulomb.”

⭐ PAGE 6 — Amp Speeds In

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Amp: “I move Coulombs every second! That’s why Current = Q / t.”

⭐ PAGE 7 — Ohm Blocks the Path

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Ohm: “I resist your movement!”

Amp: “I want to move through the wire!”

⭐ PAGE 8 — NEW SCENE: Why V = IR

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Volt: “If Ohm resists more, I must push harder.”

Theta: “So your push (V) depends on how much Amp moves (I) and how much Ohm resists (R).”

Volt: “That’s why:

$$V=IR$$

My push = Amp’s movement × Ohm’s resistance.”

⭐ PAGE 9 — Energy & Power

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Volt: “I give Joules per Coulomb.”

Amp: “I move Coulombs per second.”

Together: “Power = Joules per second = VI!”

⭐ PAGE 10 — Water Analogy

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Volt: “I’m pressure.” Amp: “I’m flow rate.” Ohm: “I’m pipe thickness.” Chargey: “Energy is total water delivered!”

⭐ PAGE 11 — Final Scene

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Volt: “I give energy per charge!” Amp: “I move charges per second!” Ohm: “I resist!” Forcey: “I push objects!” Theta: “I split angled forces!” Joule: “I’m the energy packet!” Chargey: “And I make electricity happen!”

Together: “Science is easy when you understand the story!”

📘 WORKSHEET — Joules, Voltage, Current, Resistance & Work

⭐ Section A — Joules & Energy Packets

1. What is a Joule?

2. List 3 real‑world actions that use ~1 Joule.

3. If Volt = 1V, how many Joules does each Coulomb get?

4. If Volt = 6V, how many Joules does each Coulomb get?

5. If 4 Coulombs pass through a 3V battery, find energy (W = VQ).

6. Draw Chargey receiving Joule packets from Volt.

⭐ Section B — Voltage & Coulomb

7. What does voltage measure?

8. What does 1 Coulomb represent?

9. If Volt gives 2 Joules per Coulomb, how many Joules do 10 Coulombs get?

10. Why does higher voltage mean more energy packets?

⭐ Section C — Current & Resistance

11. What does current measure?

12. If 3A flows for 2 seconds, how many Coulombs moved?

13. Why does resistance reduce current?

14. Explain why V = IR using the “push vs resistance” idea.

⭐ Section D — Power

15. Why is power measured in Joules per second?

16. If V = 10V and I = 2A, find power.

17. Draw Volt giving packets and Amp delivering them every second.

Electricity Basics

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⚡ Understanding Electricity from the Basics

Charge → Voltage → EMF → Current → Resistance → Power → Energy

Electricity becomes simple when you build it from the smallest idea: electric charge. Every other concept — voltage, current, resistance, power — is just a consequence of how charges behave.

Let’s build the entire story step by step.

🔹 1. Electric Charge — The Starting Point of Electricity

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Everything in the universe is made of atoms. Atoms contain:

• Protons → positive charge

• Electrons → negative charge

• Neutrons → no charge

Electricity happens when electrons move.

Unit of Charge

$$\boxed{{\displaystyle \text{Coulomb (C)}}}$$

Symbol:

$$\boxed{{\displaystyle Q}}$$

A single electron has a tiny charge:

$$e=1.6\times {10}^{-19}C$$

So one Coulomb contains:

$$6.24\times {10}^{18}\text{ electrons}$$

That’s billions of electrons!

🔹 2. Voltage — Energy Per Unit Charge

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Now the question: What makes electrons move?

A battery pushes electrons by creating a difference in electric potential between its terminals.

This push is called:

$$\boxed{{\displaystyle \text{Voltage (Potential Difference)}}}$$

Voltage tells us how much energy each Coulomb of charge receives.

Formula

$$\boxed{{\displaystyle V=\frac{W}{Q}}}$$

Where:

• $V$ = Voltage

• $W$ = Energy (Joules)

• $Q$ = Charge (Coulombs)

Meaning

$$1V=\frac{1J}{1C}$$

A 9V battery gives 9 Joules of energy to every 1 Coulomb of charge.

Example

A 9V battery moves 5C of charge:

$$W=VQ=9\times 5=45J$$

🔹 3. EMF — The Battery’s Maximum Ability to Supply Energy

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A battery does not create electrons. Electrons already exist in the wire.

The battery uses chemical reactions to separate charges and maintain a voltage difference.

This ability is called:

$$\boxed{{\displaystyle \text{Electromotive Force (EMF)}}}$$

Despite the name, EMF is not a force — it is energy per unit charge, just like voltage.

$$\boxed{{\displaystyle EMF=\frac{Energy}{Charge}}}$$

EMF vs Voltage

• EMF = maximum possible voltage of a battery (open circuit)

• Voltage = actual voltage when current is flowing (closed circuit)

As a battery gets used daily, chemicals get consumed, so EMF slowly decreases over time.

🔹 4. Current — Flow of Charge

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Voltage creates an electric field inside the wire. This field pushes electrons forward.

The rate at which charge flows is called:

$$\boxed{{\displaystyle \text{Current}}}$$

Formula

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

Where:

• $I$ = Current (Ampere)

• $Q$ = Charge

• $t$ = Time

Meaning

$$1A=\frac{1C}{1s}$$

One Ampere means one Coulomb of charge passes every second.

Example

10C of charge flows in 5s:

$$I=\frac{10}{5}=2A$$

🔹 5. Resistance — Opposition to Current

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Electrons collide with atoms inside a material. These collisions oppose the flow of electrons.

This property is called:

$$\boxed{{\displaystyle \text{Resistance}}}$$

Unit:

$$\boxed{{\displaystyle \mathrm{\Omega }\text{ (Ohm)}}}$$

High resistance → less current Low resistance → more current

A bulb filament has high resistance, so it heats up and glows.

🔹 6. Ohm’s Law — The Most Important Relationship

$$\boxed{{\displaystyle V=IR}}$$

Where:

• $V$ = Voltage

• $I$ = Current

• $R$ = Resistance

From this:

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

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

Example

10V battery, 5Ω resistor:

$$I=\frac{10}{5}=2A$$

🔹 7. Electrical Energy

Energy is the total work done.

From voltage:

$$V=\frac{W}{Q}$$

Rearranging:

$$\boxed{{\displaystyle W=VQ}}$$

A battery stores chemical energy and converts it into electrical energy.

🔹 8. Power — How Fast Energy Is Used

Power is the rate of energy transfer.

$$\boxed{{\displaystyle P=\frac{W}{t}}}$$

Unit:

$$\boxed{{\displaystyle W=\frac{J}{s}}}$$

A 60W bulb uses 60 Joules every second.

Deriving Power Formula

We know:

$$W=VQ$$

$$P=\frac{W}{t}=\frac{VQ}{t}$$

But:

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

So:

$$\boxed{{\displaystyle P=VI}}$$

Example

Voltage = 120V Current = 2A

$$P=120\times 2=240W$$

🔹 9. How All Concepts Connect

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Code

Charge (Q)
    ↓
Voltage (V) — energy per charge
    ↓
Current (I) — flow of charge
    ↓
Resistance (R) — controls current
    ↓
Energy (W) — total work done
    ↓
Power (P) — work done per second

🔹 Final Mental Model — Electricity as Water

Electricity	Water
Voltage	Pressure
Current	Flow rate
Resistance	Pipe thickness
Energy	Total water delivered
Power	Water delivered per second

The battery provides the push, the wire provides the path, resistance controls the flow, and the device converts electrical energy into light, heat, or motion.

Want an Illustrated Kids Version?

I can create a child‑friendly version with:

• cartoons

• simple analogies

• circuit diagrams

• practice questions

• animations (GIF-style explanations)

Just tell me the age group and style you want.

Here is the clear, Class‑8 friendly but deep explanation you asked for, Neeraj — focusing only on Energy, Work, Voltage, Current, and Power, and how they all connect through charge.

I’ll build it from the ground up so your son (and you!) get a perfect mental model.

⚡ 1. What is Work in Electricity?

In physics, work means:

Energy used to move something against a force.

In electricity, the “something” is electric charge.

So electrical work means:

Energy used to move electric charge through a circuit.

The battery uses chemical energy to push charges through wires, bulbs, motors, etc.

⚡ 2. What is Energy in Electricity?

Energy is simply:

The ability to do work.

In electricity, energy is given to charges by the battery.

The key formula is:

$$\boxed{{\displaystyle W=VQ}}$$

Where:

• $W$ = Energy (Joules)

• $V$ = Voltage (Volts)

• $Q$ = Charge (Coulombs)

This formula tells you:

Energy depends on two things:

• How much charge moves (Q)

• How much energy each charge gets (V)

So energy is not voltage and not current. Energy is the total work done when charges move.

⚡ 3. So What Exactly Is Voltage?

Voltage is:

Energy per unit charge.

$$\boxed{{\displaystyle V=\frac{W}{Q}}}$$

Voltage tells you how much energy each Coulomb of charge receives.

Think of voltage as pressure.

• High voltage → each charge gets more energy

• Low voltage → each charge gets less energy

Voltage does not tell you how many charges move. It only tells you how much energy each charge gets.

⚡ 4. What Exactly Is Current?

Current is:

How many Coulombs of charge flow per second.

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

Current tells you how fast charges are moving.

• High current → many charges moving

• Low current → few charges moving

Current does not tell you how much energy each charge has. It only tells you how many charges are moving.

⚡ 5. Putting Voltage and Current Together

Voltage = energy per charge Current = charges per second

Multiply them:

$$V\times I=\frac{W}{Q}\times \frac{Q}{t}$$

The $Q$ cancels:

$$\boxed{{\displaystyle P=VI}}$$

This gives Power.

⚡ 6. What Is Power?

Power is:

How fast energy is being used.

$$\boxed{{\displaystyle P=\frac{W}{t}}}$$

Unit:

$$\boxed{{\displaystyle 1W=1\frac{J}{s}}}$$

Power tells you how many Joules per second your device consumes.

Example

A 60W bulb uses:

$$60J\text{ every second}$$

⚡ 7. The Most Important Relationships

Energy

$$\boxed{{\displaystyle W=VQ}}$$

Current

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

Power

$$\boxed{{\displaystyle P=VI}}$$

These three formulas connect charge, voltage, current, energy, and power beautifully.

⚡ 8. The Water Analogy (Perfect for Class 8)

Electricity	Water
Voltage	Pressure
Current	Flow rate
Energy	Total water delivered
Power	Water delivered per second

Voltage

Pressure pushing water.

Current

How much water flows per second.

Energy

Total water delivered.

Power

Water delivered per second.

⚡ 9. Final Mental Model (Super Simple)

• Voltage = energy per charge

• Current = charges per second

• Energy = total work done

• Power = work done per second

Voltage gives energy to each charge. Current tells how many charges move. Together they decide power.

If you want, I can turn this into a full blog page with diagrams, or a kid‑friendly illustrated version with water‑tank drawings and circuit cartoons.

Absolutely, Neeraj — you’ve nailed the intuition, and now I’ll integrate your point clearly and explicitly into the full explanation:

Yes — Voltage (V) is the amount of energy given to ONE Coulomb of charge. So V × Q is the total energy given to Q Coulombs of charge.

And similarly:

Power tells how fast that total energy is being delivered every second.

Below is the refined, blog‑ready explanation with your correction added beautifully.

⚡ Energy, Work, Voltage, Current, and Power — The Cleanest Explanation

To understand electricity deeply, you must start from charge.

🔹 1. Voltage = Energy per Charge

Voltage is the most misunderstood concept, so let’s make it crystal clear.

Voltage (V) tells you how much energy ONE Coulomb of charge receives.

$$\boxed{{\displaystyle V=\frac{W}{Q}}}$$

Where:

• $V$ = Voltage

• $W$ = Energy

• $Q$ = Charge

This means:

If voltage is 1V, each Coulomb of charge gets 1 Joule of energy.

If voltage is 9V, each Coulomb gets 9 Joules.

So what is total energy?

If each Coulomb gets V Joules, and Q Coulombs move, then:

$$\boxed{{\displaystyle W=VQ}}$$

This is the total electrical energy delivered.

🔹 Example: Voltage as Energy per Charge

A 9V battery moves 5 Coulombs of charge.

• Each Coulomb gets 9 Joules

• Total charge = 5 Coulombs

So total energy:

$$W=VQ=9\times 5=45J$$

45 Joules of electrical energy are delivered.

🔹 2. Current = Charge Flow per Second

Current tells you how many Coulombs move each second.

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

If current is 2A:

2 Coulombs of charge pass every second.

Current does not tell you how much energy each charge has — that’s voltage’s job.

🔹 3. Power = Energy Delivered per Second

Now combine the two ideas:

• Voltage = energy per charge

• Current = charges per second

Multiply them:

$$V\times I=\left(\frac{W}{Q}\right)\times \left(\frac{Q}{t}\right)$$

The $Q$ cancels:

$$\boxed{{\displaystyle P=VI}}$$

Meaning of Power

Power tells you:

How many Joules of energy are delivered every second.

Unit:

$$\boxed{{\displaystyle 1W=1\frac{J}{s}}}$$

🔹 Example: Power

A device uses:

• Voltage = 12V

• Current = 3A

Power:

$$P=VI=12\times 3=36W$$

Meaning:

The device consumes 36 Joules every second.

🔹 4. Putting It All Together

Here is the complete chain:

Voltage (V)

Energy per charge

$$V=\frac{W}{Q}$$

Current (I)

Charge per second

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

Energy (W)

Total work done

$$W=VQ$$

Power (P)

Energy per second

$$P=VI$$

🔹 5. The Water Analogy (Perfect for Class 8)

Electricity	Water
Voltage	Pressure per drop
Current	Drops per second
Energy	Total water delivered
Power	Water delivered per second

• Voltage = how much energy each drop has

• Current = how many drops flow

• Energy = total water delivered

• Power = water delivered per second

🔹 Final Mental Model (Super Simple)

• Voltage = energy for one charge

• VQ = total energy for Q charges

• Current = how fast charges move

• Power = how fast energy is delivered

This is the cleanest way to understand electricity.

If you want, I can now create a full blog page combining all sections (charge → voltage → EMF → current → resistance → power → energy) with diagrams and analogies.

Here it is, Neeraj — a full, kid‑friendly, illustrated blog page with water‑tank diagrams, circuit cartoons, and step‑by‑step explanations. I’ve added visuals using image tags so the page feels like a real illustrated science blog.

⚡ Understanding Electricity from the Ground Up

Charge → Voltage → EMF → Current → Resistance → Energy → Power

Electricity becomes simple when you start from the smallest idea: electric charge. Every other concept — voltage, current, resistance, power — is just a consequence of how charges behave.

🌟 1. Electric Charge — The Starting Point

Matter is made of atoms. Atoms contain:

• Protons → positive charge

• Electrons → negative charge

• Neutrons → no charge

Electricity happens when electrons move.

• 
• 
• 
• 

Unit of Charge

$$\boxed{{\displaystyle \text{Coulomb (C)}}}$$

Symbol:

$$\boxed{{\displaystyle Q}}$$

A single electron has a tiny charge:

$$e=1.6\times {10}^{-19}C$$

So one Coulomb contains:

$$6.24\times {10}^{18}\text{ electrons}$$

That’s billions of electrons!

⚡ 2. Voltage — Energy Given to ONE Charge

Voltage is the “push” that gives energy to charges.

Voltage = Energy per Coulomb of charge

$$\boxed{{\displaystyle V=\frac{W}{Q}}}$$

This means:

If voltage is 1V, each Coulomb gets 1 Joule of energy. If voltage is 9V, each Coulomb gets 9 Joules.

So total energy is:

$$\boxed{{\displaystyle W=VQ}}$$

If each Coulomb gets V Joules, and Q Coulombs move, total energy is VQ.

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Example

A 9V battery moves 5 Coulombs:

$$W=VQ=9\times 5=45J$$

The battery delivers 45 Joules of energy.

🔋 3. EMF — The Battery’s Maximum Ability to Give Energy

A battery uses chemical reactions to separate charges.

This ability is called:

$$\boxed{{\displaystyle \text{Electromotive Force (EMF)}}}$$

EMF is not a force. It is energy per charge, just like voltage.

EMF vs Voltage

• EMF = maximum possible voltage (open circuit)

• Voltage = actual voltage when current flows (closed circuit)

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• 
• 
• 

As the battery is used daily, chemicals get consumed → EMF slowly decreases.

⚡ 4. Current — How Fast Charges Move

Current tells you how many Coulombs pass per second.

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

Meaning

$$1A=1\frac{C}{s}$$

One Ampere means one Coulomb passes every second.

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⚡ 5. Resistance — Opposition to Charge Flow

Electrons collide with atoms inside a material. These collisions oppose movement.

This is called:

$$\boxed{{\displaystyle \text{Resistance}}}$$

Unit:

$$\boxed{{\displaystyle \mathrm{\Omega }}}$$

A bulb filament has high resistance → it heats up and glows.

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⚡ 6. Ohm’s Law — The Most Important Relationship

$$\boxed{{\displaystyle V=IR}}$$

Where:

• $V$ = Voltage

• $I$ = Current

• $R$ = Resistance

Example

10V battery, 5Ω resistor:

$$I=\frac{10}{5}=2A$$

⚡ 7. Energy — Total Work Done

From voltage:

$$V=\frac{W}{Q}$$

Rearranging:

$$\boxed{{\displaystyle W=VQ}}$$

Energy is the total work done when charges move.

⚡ 8. Power — How Fast Energy Is Used

Power is:

Energy delivered per second

$$\boxed{{\displaystyle P=\frac{W}{t}}}$$

Since:

$$W=VQ$$

and:

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

Substitute:

$$\boxed{{\displaystyle P=VI}}$$

Meaning

Power tells you how many Joules per second your device consumes.

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Example

Voltage = 12V Current = 3A

$$P=12\times 3=36W$$

The device uses 36 Joules every second.

💧 9. Water Analogy — Perfect for Kids

Electricity	Water
Voltage	Pressure per drop
Current	Drops per second
Resistance	Narrow pipe
Energy	Total water delivered
Power	Water delivered per second

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• 
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Voltage

Pressure pushing each drop.

Current

How many drops flow per second.

Energy

Total water delivered.

Power

Water delivered per second.

🎯 10. Final Mental Model (Super Simple)

• Voltage = energy for ONE charge

• VQ = total energy for Q charges

• Current = how fast charges move

• Power = how fast energy is delivered

• Resistance = how much the wire opposes movement

• EMF = battery’s maximum ability to give energy

If you want, I can turn this into:

• a PDF‑ready layout,

• a school project poster,

• or a comic‑style version with characters explaining electricity.

Just tell me the style you want next.