Recall and use the equation for resistance R = V / I

Key Formula

The resistance of a conductor is given by $R = \dfrac{V}{I}$ where $V$ is the voltage across the conductor and $I$ is the current flowing through it.

In block form:

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

Analogy: Water Flow

Think of an electrical circuit like a water pipe:

• Voltage ($V$) is like the water pressure that pushes the water.
• Current ($I$) is like the flow rate of the water.
• Resistance ($R$) is like the size of the pipe – a narrow pipe (high resistance) lets less water (current) flow for the same pressure.

Just as a narrower pipe reduces water flow, a higher resistance reduces electrical current for a given voltage.

Worked Example

🔋 A 12 V battery is connected to a resistor. The current measured is 3 A. What is the resistance?

1. Identify the known values: $V = 12\,\text{V}$, $I = 3\,\text{A}$.
2. Insert into the formula: $R = \dfrac{V}{I} = \dfrac{12}{3}$.
3. Calculate: $R = 4\,\Omega$.

Result: The resistor has a resistance of 4 Ω ⚡️.

Exam Tips

• Always check the units – $V$ in volts, $I$ in amperes, $R$ in ohms.
• Remember that a higher voltage or a lower resistance will increase the current.
• When a question gives current and resistance, you can find voltage using $V = I \times R$.
• Use the SI prefix (kilo, milli, micro) correctly when converting units.
• Practice rearranging the formula: $I = \dfrac{V}{R}$ and $V = I \times R$.