Push harder and more current flows; put something in the way and less flows. The "something in the way" is resistance. A bulb filament or a resistor resists the flow, turning electrical energy into heat and light. Solving the law is a one-step equation, in any complete circuit.
Key idea
Ohm's law: $$V = I\,R$$ Voltage (V) = current (A) × resistance in ohms (Ω). So $I = \dfrac{V}{R}$ and $R = \dfrac{V}{I}$.
Why it works
For many materials, doubling the voltage doubles the current: current and voltage are proportional. The resistance is the constant ratio $\dfrac{V}{I}$, a property of the resistor itself, set by its material, length and thickness. A thin, long wire has more resistance than a short, thick one, just as a narrow pipe lets less water through.
Worked example: Find the current
A 12 V battery is connected to a 4 Ω resistor. Find the current.
- $I = \dfrac{V}{R} = \dfrac{12\,\mathrm{V}}{4\,\Omega} = 3\,\mathrm{A}$.
Answer: 3 A
Worked example: Find the resistance
A lamp draws 0.5 A from a 6 V supply. What is its resistance?
- $R = \dfrac{V}{I} = \dfrac{6\,\mathrm{V}}{0.5\,\mathrm{A}} = 12\,\Omega$.
Answer: 12 Ω
Common mistake
Thinking a resistor's resistance changes when the current through it changes. For an ordinary resistor, if you double the voltage, the current doubles too, and $R = \dfrac{V}{I}$ stays the same. Resistance depends on the resistor, not on what you connect it to. (A bulb filament is an exception in one way: its resistance rises as it heats up.)
Measure currents and voltages yourself in the Circuit Builder.