Three key quantities
| Quantity | Symbol | Unit | Analogy (water in pipes) | Measured with |
|---|---|---|---|---|
| Electric current | I | ampere (A) | How much water flows per second | Ammeter (in series) |
| Voltage (potential difference) | V | volt (V) | Water pressure from a pump | Voltmeter (in parallel) |
| Resistance | R | ohm (Ω) | Narrowness of the pipe | Ohmmeter |
- Current is the flow of electrons, but by convention we draw current flowing from + to −.
- A battery provides voltage: it gives energy to each charge.
- Loads (bulbs, motors) have resistance and convert electrical energy to other forms.
Ohm’s law
V = I × R
Rearranged: I = V ÷ R, R = V ÷ I
Example: A 9 V battery connects to a 3 Ω resistor. Current = 9 ÷ 3 = 3 A.
Resistance depends on:
- material (copper is low, nichrome is high)
- length (longer = more resistance)
- thickness (thinner = more resistance)
- temperature (hotter metal = more resistance)
Circuit diagrams
Standard symbols make circuits easy to draw: a long and short line for a cell, a circle with a cross for a bulb, a rectangle for a resistor, a gap for an open switch, and circles with A or V for meters.
Series circuits
A series circuit has one path.
| Property | Rule |
|---|---|
| Current | Same everywhere: I₁ = I₂ = I₃ |
| Voltage | Shared: V_total = V₁ + V₂ + V₃ |
| Resistance | Adds: R_total = R₁ + R₂ + R₃ |
| If one bulb fails | Whole circuit stops |
| Adding bulbs | Each gets dimmer |
Example: 2 Ω and 4 Ω resistors in series with 12 V. R_total = 6 Ω; I = 12 ÷ 6 = 2 A. Voltage across 4 Ω = 2 × 4 = 8 V.
Parallel circuits
A parallel circuit has multiple branches.
| Property | Rule |
|---|---|
| Voltage | Same across each branch |
| Current | Splits: I_total = I₁ + I₂ + I₃ |
| Resistance | 1/R_total = 1/R₁ + 1/R₂ + …; total is less than the smallest |
| If one bulb fails | Others stay on |
| Adding bulbs | Each stays bright, but the battery drains faster |
Homes are wired in parallel so each appliance gets the full 120 V and works independently.
Electrical power and energy
P = V × I (watts)
Energy = P × t (joules, or kilowatt-hours)
Example: A 1200 W hair dryer used for 0.5 hours uses 0.6 kWh. At 13 cents/kWh, that costs about 8 cents.
Safety devices
- Fuses melt and circuit breakers trip if current gets too high, preventing fires.
- Ground wires give stray current a safe path.
- GFCI outlets (in kitchens and bathrooms) cut power within milliseconds if current leaks.
Magnets and magnetic fields
- Magnets have north and south poles; like poles repel, opposite poles attract.
- A magnetic field surrounds a magnet. Field lines go from north to south outside the magnet.
- Earth’s magnetic field comes from moving molten iron in its outer core. It protects us from solar wind and makes compasses work. Earth’s geographic North Pole is actually near a magnetic south pole, which is why the north end of a compass points to it!
Electromagnetism
- A current-carrying wire produces a circular magnetic field around it.
- Coiling the wire (a solenoid) concentrates the field. Adding an iron core makes an electromagnet.
- Stronger electromagnet: more turns, more current, an iron core.
Electric motors
A current-carrying coil in a magnetic field feels a force and spins. Motors convert electrical energy into kinetic energy. They’re in fans, blenders, electric cars and hard drives.
Generators
Electromagnetic induction, discovered by Michael Faraday in 1831: moving a magnet in or out of a coil (or spinning a coil in a field) produces a voltage. Generators convert kinetic energy into electrical energy. Almost all electricity, from hydro dams to wind turbines, is generated this way.
Common mistakes
- Thinking current gets used up. Current is the same in and out; energy is what’s transferred.
- Connecting a voltmeter in series or an ammeter in parallel.
- Thinking adding resistors in parallel increases total resistance. It decreases it.
Try it yourself
- Find the current through a 12 Ω bulb connected to 6 V.
- Three 6 Ω resistors are in series with 9 V. Find R_total and the current.
- The same three resistors in parallel: find R_total and the total current.
- Why do your headlights dim slightly when you start a car?
(Answers: 0.5 A; 18 Ω, 0.5 A; 2 Ω, 4.5 A; the starter motor draws a large current, lowering the voltage available to other parallel loads)
Quick recap
- V = IR links voltage, current and resistance.
- Series: same current, voltages add, resistances add.
- Parallel: same voltage, currents add, total resistance drops.
- P = VI gives electrical power.
- Currents make magnetic fields; changing magnetic fields make currents.