Resistance (\$R\$) is a property of a material that opposes the flow of electric current. It is measured in ohms (Ω).
2. Factors Affecting Resistance
Material – different materials have different resistivities.
Length (\$L\$) – resistance increases with length.
Cross‑sectional area (\$A\$) – resistance decreases as the area increases.
Temperature – for most conductors, resistance increases with temperature.
3. Resistivity and the Resistance Formula
The intrinsic property of a material is its resistivity (\$\rho\$). The resistance of a uniform conductor is given by:
\$R = \rho \frac{L}{A}\$
4. Relationship Between Power, Current, Voltage and Resistance
Starting from the definition of power:
\$P = I V\$
Using Ohm’s law (\$V = I R\$) we can derive two additional useful forms:
Substituting \$V = I R\$ into \$P = I V\$ gives:
\$P = I (I R) = I^{2} R\$
Solving Ohm’s law for \$I = \frac{V}{R}\$ and substituting into \$P = I V\$ gives:
\$P = \left(\frac{V}{R}\right) V = \frac{V^{2}}{R}\$
5. Summary Table of Key Formulas
Quantity
Formula
Notes
Resistance
\$R = \rho \frac{L}{A}\$
Ω (ohms)
Ohm’s Law
\$V = I R\$
Voltage in volts (V)
Power (basic)
\$P = I V\$
Watts (W)
Power (current form)
\$P = I^{2} R\$
Useful when current is known
Power (voltage form)
\$P = \frac{V^{2}}{R}\$
Useful when voltage is known
6. Example Problem
Question: A heater element has a resistance of \$10\ \Omega\$ and is connected to a \$240\ \text{V}\$ supply. Calculate the power dissipated by the heater.