Electrical Resistance and Ohm's Law

• Ohm's Law Formula: The relationship connects resistance ($R$), voltage ($V$), and current ($I$).

Formula: $R = \frac{V}{I}$ or $V = I \times R$

• Linearity: For fixed resistors, the ratio $\frac{V}{I}$ remains constant regardless of the voltage applied, provided the temperature is stable.

• Proportionality: If resistance is constant, doubling the voltage doubles the current.

• Length ($L$): Resistance is directly proportional to the length of the wire ($R \propto L$). A longer wire presents a longer path for electrons, leading to more collisions.

• Cross-Sectional Area ($A$): Resistance is inversely proportional to the cross-sectional area ($R \propto \frac{1}{A}$). A thicker wire provides more space for electrons to flow, reducing the likelihood of collisions.

• Temperature: For metal conductors, increasing temperature increases the vibration of lattice ions, which increases the frequency of collisions and thus increases resistance.

• Graph Axes: Always check which variable is on the y-axis. Standard I-V graphs have Current ($I$) on the y-axis. If Voltage ($V$) is on the y-axis, the gradient represents Resistance ($R$), not $1/R$.

• Describing Trends: When explaining the filament lamp graph, link the change in gradient to the change in resistance. A flattening curve (decreasing gradient on an I-V graph) means increasing resistance.

• Unit Conversion: Watch for milli-amps ($mA$). Always convert to Amps ($A$) before using $V=IR$. $1 mA = 0.001 A$.

• Calculations: If asked to find resistance from a graph at a specific point, use the coordinates $(V, I)$ at that point, NOT the gradient of the tangent.