Current & Voltage Relationships

The Fundamental Proportionality: Ohm's Law states that for many materials, the current flowing through a conductor is directly proportional to the voltage applied across it, provided physical conditions like temperature remain constant.

Mathematical Expression: The relationship is defined by the formula $V = IR$, where voltage is the product of current and resistance.

Linearity: A component that obeys Ohm's Law is called an ohmic or linear component, characterized by a constant resistance regardless of the applied voltage.

Calculating Unknowns: To find a specific value, rearrange the Ohm's Law formula: $I = \frac{V}{R}$ to find current, or $R = \frac{V}{I}$ to find resistance.

Power Calculation: The rate at which electrical energy is converted into other forms (like heat) is given by $P = VI$. By substituting Ohm's Law, this can also be expressed as $P = I^2R$ or $P = \frac{V^2}{R}$.

Unit Consistency: Always ensure values are in base units (Amps, Volts, Ohms) before calculating. For example, convert $5$ mA to $0.005$ A and $2$ k$\Omega$ to $2000$ $\Omega$.

Check the Origin: In I-V graphs, always verify if the line passes through $(0,0)$. A linear component must have zero current when there is zero voltage.

Gradient Interpretation: On a graph of Current ($y$-axis) vs. Voltage ($x$-axis), the gradient represents the conductance ($G$), while the reciprocal of the gradient represents the resistance ($R$).

Sanity Check: If resistance increases, current must decrease for a fixed voltage. If your calculated current is higher than expected after adding resistance, re-check your division.

Prefix Awareness: Examiners frequently use 'milli' ($10^{-3}$) and 'kilo' ($10^3$). A common mistake is forgetting to convert these, leading to answers that are off by factors of $1000$ or $1,000,000$.

The 'Constant Resistance' Myth: Students often assume all components are ohmic. In reality, components like filament bulbs increase in resistance as they get hotter due to increased atomic vibrations.

Power Formula Confusion: Using $P = I^2R$ when you only know $V$ and $R$ without calculating $I$ first can lead to errors. It is safer to use the version of the power formula that matches your known variables directly.

Direction of Current: Remember that 'conventional current' flows from positive to negative, even though electrons actually flow from negative to positive.