# Current, Voltage, Resistance and Ohm's Law

> The three key quantities in every circuit and the simple law that links them.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/current-voltage-resistance/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The water slide
At the water park, Ethan's little sister asked how electricity works. He pointed at the giant water slide.

"See the pump at the bottom? It lifts water up to the top. That is like a **battery**. It gives the water a push."

"The water rushing down the slide is like **current**. How much water flows past each second."

"The height of the slide is like **voltage**. Higher slide, more push."

"And see where the slide gets narrow and twisty? The water slows down there. That's **resistance**."

It is not a perfect picture, but it gets you surprisingly far.

**In short:** Current is the flow of electric charge, measured in amps (A). Voltage is the push that drives it, in volts (V), and resistance is how much a component opposes it, in ohms (Ω). Ohm's law links them: $V = IR$.

## Electric current

**Current** is the **flow of electric charge**. In a wire, the moving charges are **electrons**.

- Symbol: $I$
- Unit: **ampere (A)**, often called "amps". Small currents are in milliamps (mA): 1000 mA = 1 A.
- Measured with an **ammeter**, connected **in series** (in line with the component).

A current only flows if there is a **complete loop** (a closed circuit) and something to push the charge, like a battery.

### Key idea: Conventional current
Scientists decided current flows from **+ to −** before electrons were discovered. Electrons actually flow the other way, from − to +. We still draw **conventional current** going from + to −. Both describe the same thing.

## Voltage (potential difference)

**Voltage** is the **push** that drives current around a circuit. More precisely, it is the **energy given to or used by each unit of charge**.

- Symbol: $V$
- Unit: **volt (V)**
- Measured with a **voltmeter**, connected **in parallel** (across the component, on a side branch).

A battery **gives** energy to the charges. Components like bulbs **use** that energy. A 9 V battery gives 9 joules to every coulomb of charge that passes through it.

## Resistance

**Resistance** is how much a component **opposes** the flow of current.

- Symbol: $R$
- Unit: **ohm (Ω)**

Resistance is like friction for electricity. When current pushes through a resistance, some electrical energy becomes heat. This is how toasters, kettles and heaters work.

The resistance of a wire is **bigger** when the wire is:
- **longer**
- **thinner**
- **hotter** (for most metals)
- made of a material that conducts poorly (like nichrome instead of copper)

## Ohm's law

For many components, the current is **directly proportional** to the voltage, as long as the temperature stays the same.

$$V = I \times R$$

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

### Worked example: Finding the current
A 12 V battery is connected to a 4 Ω resistor.

$$I = \frac{V}{R} = \frac{12}{4} = 3 \text{ A}$$

### Worked example: Finding the resistance
A torch bulb draws 0.5 A from a 3 V battery.

$$R = \frac{V}{I} = \frac{3}{0.5} = 6 \ \Omega$$

## I-V graphs

An **I-V graph** plots current against voltage.

- **Ohmic resistor** (constant temperature): a **straight line through the origin**. The resistance is constant.
- **Filament bulb**: a **curve that flattens**. As the bulb gets hotter, its resistance increases, so the current grows less and less.
- **Diode**: current flows only one way, and only once the voltage passes about 0.7 V.

### Watch out: Ammeter and voltmeter mix-up
**A**mmeters go **a**long the circuit (series). **V**oltmeters go **across** a component (parallel). An ammeter connected in parallel can short the circuit and blow its fuse.

**Mind map**

```text
Electricity basics
  Current I
    Flow of charge
    Amps (A)
    Ammeter in series
  Voltage V
    Push, energy per charge
    Volts (V)
    Voltmeter in parallel
  Resistance R
    Opposes current
    Ohms (Ω)
    Longer, thinner = more
  Ohm's law
    V = IR
    Straight I-V line
    Bulb curve
```

### Year 11: Charge, energy and power
Current is the rate of flow of charge:

$$I = \frac{q}{t} \qquad (q \text{ in coulombs, C})$$

Voltage is energy per charge:

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

**Electrical power** is the rate of energy use:

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

Energy used: $E = Pt = VIt$. Electricity companies charge per **kilowatt hour** (kWh), the energy used by a 1 kW device running for 1 hour: $1 \text{ kWh} = 3.6 \times 10^6$ J.

Resistance of a wire: $R = \dfrac{\rho L}{A}$, where $\rho$ is resistivity, $L$ length and $A$ cross-sectional area.

### Year 12: Superconductors and drift velocity
Electrons in a wire actually move very slowly, drifting at less than a millimetre per second. The signal travels fast because the electric field moves through the wire at nearly the speed of light, pushing all the electrons at once. The drift velocity is $v = \dfrac{I}{nqA}$.

Some materials, cooled below a **critical temperature**, have **zero resistance**. These **superconductors** carry current with no energy loss and push magnetic fields out (the Meissner effect). They are used in MRI machines, particle accelerators and maglev trains.

## Quick summary

- **Current** ($I$, amps) is the flow of charge. Measure with an ammeter **in series**.
- **Voltage** ($V$, volts) is the push, or energy per charge. Measure with a voltmeter **in parallel**.
- **Resistance** ($R$, ohms) opposes current. Longer, thinner, hotter wires have more.
- **Ohm's law**: $V = IR$.
- Ohmic resistor: straight I-V line. Filament bulb: curve, because resistance rises as it heats.

## Quiz

Try these questions from the chapter quiz.

1. The unit of electric current is the:
   - A. Volt
   - B. Ampere
   - C. Ohm
   - D. Watt
   - Answer: B. Ampere. Current is measured in amperes (A).

2. A voltmeter must be connected:
   - A. In series
   - B. In parallel across the component
   - C. Only next to the battery
   - D. Anywhere in the circuit
   - Answer: B. In parallel across the component. A voltmeter measures the difference across a component, so it sits on a side branch.

3. A 6 Ω resistor has 2 A flowing through it. The voltage across it is:
   - A. 3 V
   - B. 8 V
   - C. 12 V
   - D. 0.33 V
   - Answer: C. 12 V. V = IR = 2 × 6 = 12 V.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/current-voltage-resistance/#quiz