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\$.