Electricity and Magnetism

📖 Learn

Electricity involves the behavior of electric charges and the forces between them. Magnetism involves magnetic fields and forces. These phenomena are deeply connected—changing electric fields create magnetic fields, and changing magnetic fields create electric fields.

Electric Charge

Two types: positive (+) and negative (-)
Like charges repel; opposite charges attract
Unit: Coulomb (C)
Charge is conserved—it cannot be created or destroyed
Elementary charge (electron/proton): e = 1.6 × 10⁻¹⁹ C

Coulomb's Law

The electric force between two point charges:

F = k(q₁q₂)/r²

Where: k = 9 × 10⁹ N·m²/C², q = charge, r = distance between charges

Force decreases with the square of distance (inverse square law).

Electric Current and Circuits

Quantity	Symbol	Unit	Definition
Current	I	Ampere (A)	Rate of charge flow (I = Q/t)
Voltage	V	Volt (V)	Electric potential difference ("push" for charges)
Resistance	R	Ohm (Ω)	Opposition to current flow
Power	P	Watt (W)	Rate of energy transfer

Ohm's Law

V = IR

Voltage equals current times resistance.

Rearranged: I = V/R (current) or R = V/I (resistance)

Electric Power

P = IV = I²R = V²/R

Power is energy per unit time. Electric bills are based on kilowatt-hours (kWh).

Series and Parallel Circuits

	Series Circuit	Parallel Circuit
Current	Same through all components	Splits among branches
Voltage	Divides among components	Same across all branches
Total Resistance	R_total = R₁ + R₂ + R₃...	1/R_total = 1/R₁ + 1/R₂ + 1/R₃...
If one breaks	Entire circuit stops	Other branches still work

Magnetism Basics

Magnets have north (N) and south (S) poles
Like poles repel; opposite poles attract
Magnetic field lines go from N to S outside the magnet
Earth acts as a giant magnet (geographic north is magnetic south)
Breaking a magnet creates two smaller magnets—you can't isolate a single pole

Electromagnetism

Key discoveries:

Moving charges (current) create magnetic fields
Changing magnetic fields create electric fields (electromagnetic induction)
A current-carrying wire in a magnetic field experiences a force

Applications

Device	Principle
Electromagnet	Current through coiled wire creates controllable magnetic field
Electric Motor	Current-carrying coil in magnetic field rotates (electrical → mechanical)
Generator	Rotating coil in magnetic field induces current (mechanical → electrical)
Transformer	Changes voltage using electromagnetic induction between coils

💡 Examples

Work through these electricity and magnetism problems.

Example 1: Ohm's Law

Problem: A 12V battery is connected to a 4Ω resistor. What current flows through the circuit?

Solution

Given: V = 12V, R = 4Ω

Using Ohm's Law: I = V/R = 12/4 = 3 A

Example 2: Electric Power

Problem: A light bulb draws 2A of current from a 120V outlet. What is its power consumption?

Solution

Given: I = 2A, V = 120V

Using P = IV: P = (2)(120) = 240 W

Example 3: Series Resistance

Problem: Three resistors (2Ω, 3Ω, and 5Ω) are connected in series to a 20V battery. (a) What is the total resistance? (b) What current flows?

Solution

(a) Total resistance in series:

R_total = R₁ + R₂ + R₃ = 2 + 3 + 5 = 10Ω

(b) Current:

I = V/R_total = 20/10 = 2 A

Example 4: Parallel Resistance

Problem: Two 6Ω resistors are connected in parallel. What is the equivalent resistance?

Solution

For parallel resistors:

1/R_total = 1/R₁ + 1/R₂ = 1/6 + 1/6 = 2/6 = 1/3

R_total = 3Ω

Note: Parallel resistance is always less than the smallest individual resistor.

Example 5: Energy Cost

Problem: A 100W light bulb runs for 5 hours. If electricity costs $0.12 per kWh, what is the cost?

Solution

Energy used: E = P × t = 100W × 5h = 500 Wh = 0.5 kWh

Cost: 0.5 kWh × $0.12/kWh = $0.06 (6 cents)

✏️ Practice

Solve these electricity and magnetism problems.

1. What is the current through a 10Ω resistor connected to a 5V source?

2. A device draws 0.5A from a 9V battery. What is its resistance?

3. What voltage is needed to push 3A through a 4Ω resistor?

4. Calculate the power consumed by a device with 2A current and 6Ω resistance.

5. Three 9Ω resistors are connected in series. What is the total resistance?

6. Three 9Ω resistors are connected in parallel. What is the total resistance?

7. A 60W bulb operates for 8 hours per day for 30 days. How many kWh of energy does it use?

8. Two charges of +2C and +3C are separated by 0.5m. Is the force between them attractive or repulsive?

9. In a series circuit, the current through one resistor is 2A. What is the current through the other resistors?

10. A toaster draws 10A from a 120V outlet. What is its power rating?

Answer Key

I = V/R = 5/10 = 0.5 A
R = V/I = 9/0.5 = 18Ω
V = IR = (3)(4) = 12 V
P = I²R = (2)²(6) = 4 × 6 = 24 W
R_total = 9 + 9 + 9 = 27Ω
1/R = 1/9 + 1/9 + 1/9 = 3/9 = 1/3; R_total = 3Ω
E = 60W × 8h × 30 days = 14,400 Wh = 14.4 kWh
Repulsive — Both charges are positive (like charges repel)
2A — In series circuits, current is the same through all components
P = IV = (10)(120) = 1200 W

✅ Check Your Understanding

1. Why does parallel resistance end up being less than the smallest individual resistor?

Show Answer

In a parallel circuit, current has multiple paths to flow through. Adding more paths (even if they have resistance) makes it easier for current to flow overall—like adding more lanes to a highway reduces traffic congestion. Each parallel resistor provides an additional pathway, reducing the total opposition to current flow.

2. Why do we use high voltage for long-distance power transmission?

Show Answer

Power lost to heat in transmission lines equals I²R. To transmit the same power (P = IV), you can either use high current with low voltage, or low current with high voltage. Since power loss depends on I², using high voltage (and therefore low current) dramatically reduces energy wasted as heat. That's why power lines operate at hundreds of thousands of volts.

3. Explain how a generator works in terms of electromagnetic induction.

Show Answer

A generator converts mechanical energy to electrical energy using electromagnetic induction. When a coil of wire rotates in a magnetic field (or a magnet rotates near a coil), the magnetic flux through the coil changes. This changing magnetic flux induces an electric current in the wire. The faster the rotation, the more the flux changes, and the greater the induced current.

4. If you cut a bar magnet in half, what happens to its poles?

Show Answer

Each half becomes a complete magnet with its own north and south poles. You cannot isolate a single magnetic pole—they always come in pairs. If you keep cutting, you'll just get smaller and smaller magnets, each with both poles. This is fundamentally different from electric charges, where positive and negative charges can exist separately.

🚀 Next Steps

Review any concepts that felt challenging
Move on to the next lesson when ready
Return to practice problems periodically for review