How Do You Calculate Electrical Power Dissipated by a Resistor?

For IB Physics SL and HL, electrical power dissipated by a resistor is calculated with $P=IV$. If resistance is given, Ohm's law produces the equivalent forms $P=I^2R$ and $P=\frac{V^2}{R}$.

Reasoning and Method

Electrical power is the rate at which electrical energy is transferred by a circuit component:

$$P=\frac{\Delta E}{\Delta t}$$

In a resistor, this energy is transferred mainly into internal energy through heating.

Potential difference is energy transferred per unit charge, $V=\frac{W}{q}$, while current is charge flow per unit time, $I=\frac{\Delta q}{\Delta t}$. Multiplying them gives , because joules per coulomb multiplied by coulombs per second gives joules per second.

Substituting $V=IR$ into $P=IV$ gives $P=I^2R$. Alternatively, substituting gives . These relationships apply to the resistor's potential difference and current, not automatically to the whole circuit.

The SI unit is the watt (W), where $1\,\text{W}=1\,\text{J s}^{-1}$.

Worked Example

A $6.0\,\Omega$ resistor has a potential difference of $12\,\text{V}$ across it. The most direct equation is:

$$P=\frac{V^2}{R}=\frac{12^2}{6.0}=24\,\text{W}$$

The current is also $I=\frac{V}{R}=2.0\,\text{A}$, so $P=IV=(2.0)(12)=24\,\text{W}$, confirming the result.

A common misconception is that power is the total energy dissipated. Power is a rate; energy transferred over time $t$ is $E=Pt$. For fixed current, increasing resistance increases power, but for fixed voltage, increasing resistance decreases power.

Be careful when interpreting changes in resistance. If a resistor is connected to a constant-voltage supply, $P=\frac{V^2}{R}$, so doubling $R$ halves $$. If current is held constant, , so doubling doubles . Always identify which quantity is controlled before predicting a change in power.

IB Exam Technique

For a Calculate question, show the selected equation, substitution, and numerical answer. Choose the equation matching the given quantities and use SI units. These equations appear in the IB Physics data booklet under B.5 Current and circuits, so examinations test correct selection and application rather than memorization.