How Do You Calculate Resistance (R = V/I)?

To calculate resistance, divide the potential difference across a component by the current through it:

$$R=\frac{V}{I}$$

Resistance is measured in ohms (Ω), potential difference in volts (V), and current in amperes (A). This is part of IB Physics B.5 Current and circuits and applies to both SL and HL.

Resistance measures how strongly a component opposes electric current. Potential difference is the energy transferred per unit charge, while current is the rate of flow of charge. Therefore, for the same potential difference, a smaller current corresponds to a larger resistance. Rearranging the relationship also gives $V=IR$ and $I=\frac{V}{R}$.

The Method

1. Identify the potential difference, $V$, across the component.
2. Identify the current, $I$, through the component.
3. Convert the current into amperes if necessary.
4. Substitute into $R=\frac{V}{I}$.

The measured potential difference and current must refer to the same component and operating conditions. In a circuit, connect the voltmeter in parallel across the component and the ammeter in series. This makes the measured quantities appropriate for the ratio.

For example, a resistor has a potential difference of $12\text{ V}$ across it and carries a current of $0.40\text{ A}$:

$$R=\frac{12}{0.40}=30\,\Omega$$

If the current is given in milliamperes, convert it first. For a component with $V=6.0\text{ V}$ and $I=200\text{ mA}$:

$$200\text{ mA}=0.200\text{ A}$$ $$R=\frac{6.0}{0.200}=30\,\Omega$$

A useful unit relationship is:

$$1\,\Omega=1\,\frac{\text{V}}{\text{A}}$$

A common misconception is that $R=V/I$ means every component obeys Ohm's law. The ratio (V/I) gives the resistance at a particular operating point, but an ohmic conductor has constant resistance only when its physical conditions, especially temperature, remain constant. A filament lamp is non-ohmic because its resistance changes as its temperature changes.

IB Exam Technique

For a Calculate question, show the equation, substitution, and final answer. Check prefixes carefully: dividing by a current left in milliamperes produces a factor-of-1000 error. In graph questions, if potential difference is on the vertical axis and current is on the horizontal axis, the gradient $\frac{\Delta V}{\Delta I}$ gives resistance.