Voltage, Current and Resistance

The three numbers that describe any circuit

Whenever electricity flows, three quantities describe what is going on: voltage, current and resistance. Get comfortable with these three and you can predict and explain almost any simple circuit. They are not separate, unrelated ideas — they are tightly linked, and one neat equation called Ohm's law connects all three.

This lesson defines each quantity carefully, shows how they relate, and works through real calculations. If you have not met circuits yet, the loop idea is explained in how electric circuits work.

Current: the flow of charge

Electricity is the movement of electric charge. In a metal wire, the charge is carried by electrons — tiny negative particles that drift through the metal when pushed.

Current is the rate of flow of charge: how much charge passes a given point each second. A large current means a lot of charge flowing every second; a small current means only a trickle. Current is measured in amperes, usually shortened to amps (A). We use the symbol I for current (from the French intensité).

A key fact that surprises many students: current is not used up as it goes round a circuit. The same amount of charge that flows out of one battery terminal flows back into the other. The charge is recycled around the loop endlessly — what the battery actually provides is energy, not charge.

Voltage: the push that supplies energy

Voltage is the push that drives the current around the circuit. More precisely, voltage measures the energy given to each unit of charge. A higher voltage gives each charge more energy and pushes harder, producing a bigger current (if nothing else changes).

Voltage is measured in volts (V) and uses the symbol V. A battery or power supply is the source of voltage. A 1.5 V cell gives a gentle push; a 9 V battery pushes harder; mains supplies are far higher and dangerous.

Two useful points:

• Voltage is always measured across two points — it is a difference. We often say "potential difference" for exactly this reason. A voltmeter is connected across a component.
• As charge passes through a component such as a bulb, it gives up energy (which becomes light and heat), so there is a voltage across that component too.

Resistance: how much the flow is opposed

Resistance is how strongly a component opposes the flow of charge. A thin, long, or poorly-conducting wire has high resistance and lets little current through; a thick, short copper wire has very low resistance and lets current flow freely.

Resistance is measured in ohms (Ω) and uses the symbol R. What causes it? As electrons move through a material, they keep colliding with the fixed atoms, losing some energy each time. Those collisions both slow the current and heat the material. That is why a high-resistance component such as a filament or a kettle element gets hot — the resistance turns electrical energy into heat.

The water analogy

A flowing-water picture makes all three click together:

Electrical idea	Water idea
Voltage (the push)	Water pressure from a pump or tall tank
Current (rate of flow)	Amount of water flowing per second
Resistance (opposition)	A narrow section of pipe restricting the flow

Turn up the pump pressure (voltage) and more water flows (current). Pinch the pipe (raise resistance) and less water flows. This is exactly how voltage, current and resistance behave — and it leads straight to Ohm's law.

Ohm's law: V = I × R

The three quantities are linked by Ohm's law:

V = I × R   (voltage = current × resistance)

The same equation can be rearranged to find whichever quantity you need:

• To find current: I = V ÷ R
• To find resistance: R = V ÷ I

Read what the equation tells you:

• Raise the voltage (keep R fixed) → current increases. More push, more flow.
• Raise the resistance (keep V fixed) → current decreases. More opposition, less flow.

A handy memory aid is the VIR triangle: write V on top, with I and R side by side below. Cover the quantity you want and the triangle shows the formula — cover V and you see I × R; cover I and you see V over R; cover R and you see V over I.

Worked examples

Example 1 — find the current. A 9 V battery is connected across a 30 Ω resistor. I = V ÷ R = 9 ÷ 30 = 0.3 A.

Example 2 — find the resistance. A torch bulb carries 0.25 A when connected to a 5 V supply. R = V ÷ I = 5 ÷ 0.25 = 20 Ω.

Example 3 — find the voltage. A current of 2 A flows through a 4 Ω heating element. V = I × R = 2 × 4 = 8 V.

Example 4 — predict a change. A bulb runs at 6 V drawing 0.5 A, so its resistance is R = 6 ÷ 0.5 = 12 Ω. If the voltage is halved to 3 V (and resistance stays roughly the same), the current becomes I = 3 ÷ 12 = 0.25 A — half as much. Halving the push halves the flow, just as Ohm's law predicts.

Ohmic and non-ohmic components

A component is called ohmic if its resistance stays constant, so current is exactly proportional to voltage — a graph of current against voltage is a straight line through the origin. A plain metal wire at constant temperature behaves this way.

Not everything does. A filament bulb heats up as more current flows, and its resistance rises with temperature, so its current–voltage graph curves. Knowing whether a component is ohmic tells you whether you can trust V = I × R with a single fixed value of R.

Try it yourself! 🧪

Measure Ohm's law for real — low voltage only. Never use mains electricity; use only batteries of 1.5–4.5 V.

You need: a 1.5 V cell and a 4.5 V battery (or a battery pack you can set to different voltages), a fixed resistor (about 47 Ω) or a small bulb, connecting wires, and — if available — a multimeter that measures volts and amps.

1. Connect the cell to the resistor in a simple loop. Use the multimeter as an ammeter in series to read the current, and as a voltmeter across the resistor to read the voltage.
2. Record V and I. Calculate R = V ÷ I.
3. Swap to the higher-voltage battery. Read V and I again. The current should rise roughly in proportion to the voltage if the resistor is ohmic.
4. Calculate R each time. For a fixed resistor you should get nearly the same resistance — confirming Ohm's law. For a bulb, R will rise as it heats up, showing non-ohmic behaviour.

⚠️ Safety: Keep voltages at battery level (1.5–4.5 V). Resistors and bulbs can get warm — do not touch a glowing filament. Never connect meters or homemade circuits to wall sockets.

You have now measured voltage, current and resistance directly and tested Ohm's law with your own readings — the foundation of all circuit analysis.