Resistance (\$R\$) is a property of a material that opposes the flow of electric current. It is measured in ohms (Ω). The higher the resistance, the less current will flow for a given voltage.
Key Relationships
Ohm’s Law: \$V = I R\$
Re‑arranged for resistance: \$R = \dfrac{V}{I}\$
Resistivity formula: \$R = \rho \dfrac{L}{A}\$ where
\$\rho\$ = resistivity of the material (Ω·m)
\$L\$ = length of the conductor (m)
\$A\$ = cross‑sectional area (m²)
Factors that Influence Resistance
Material: Conductors (e.g., copper) have low resistivity; insulators have high resistivity.
Length (\$L\$): Resistance is directly proportional to length.
Cross‑sectional area (\$A\$): Resistance is inversely proportional to area.
Temperature: For most metals, resistance increases with temperature.
Using the Equation \$R = \dfrac{V}{I}\$
To find any one of the three quantities (voltage, current, resistance) you need the other two.
Known Quantity
Formula to Find Unknown
Example
Voltage (\$V\$) and Current (\$I\$)
\$R = \dfrac{V}{I}\$
If \$V = 12\ \text{V}\$ and \$I = 3\ \text{A}\$, then \$R = 4\ \Omega\$.
Resistance (\$R\$) and Current (\$I\$)
\$V = I R\$
If \$R = 5\ \Omega\$ and \$I = 2\ \text{A}\$, then \$V = 10\ \text{V}\$.
Voltage (\$V\$) and Resistance (\$R\$)
\$I = \dfrac{V}{R}\$
If \$V = 9\ \text{V}\$ and \$R = 3\ \Omega\$, then \$I = 3\ \text{A}\$.
Worked Example
Problem: A copper wire 2.0 m long has a cross‑sectional area of \$1.0 \times 10^{-6}\ \text{m}^2\$. The resistivity of copper is \$1.68 \times 10^{-8}\ \Omega\!\cdot\!\text{m}\$. Calculate the resistance of the wire.
Solution:
Write the resistivity formula: \$R = \rho \dfrac{L}{A}\$.
Confusing the symbols: \$V\$ is voltage, \$I\$ is current, \$R\$ is resistance.
Using the wrong units – always keep voltage in volts (V), current in amperes (A), resistance in ohms (Ω).
For the resistivity formula, ensure length and area are in metres (m) and square metres (m²) respectively.
Remember that \$R = V/I\$ only applies to ohmic (linear) conductors within their operating range.
Quick Revision Table
Quantity
Symbol
Unit
Formula
Resistance
\$R\$
Ω (ohm)
\$R = \dfrac{V}{I}\$
Voltage
\$V\$
V (volt)
\$V = I R\$
Current
\$I\$
A (ampere)
\$I = \dfrac{V}{R}\$
Resistivity
\$\rho\$
Ω·m
\$R = \rho \dfrac{L}{A}\$
Suggested diagram: A simple circuit showing a battery, a resistor, an ammeter (in series) and a voltmeter (across the resistor). Label voltage \$V\$, current \$I\$, and resistance \$R\$.