AcademyCurrent and Resistance
Academy
Electric Power
Level 1 - Physics topic page in Current and Resistance.
Principle
Electric power is the rate at which electrical energy is transferred by charges moving through a potential difference.
Notation
\(P\)
electric power
\(\mathrm{W}\)
\(\Delta U\)
energy transferred
\(\mathrm{J}\)
\(\Delta t\)
time interval
\(\mathrm{s}\)
\(I\)
current
\(\mathrm{A}\)
\(V\)
potential difference
\(\mathrm{V}\)
\(R\)
resistance
\(\mathrm{\Omega}\)
Method
Derivation 1: Build power from energy per charge
A potential difference gives energy transfer per charge. Current gives charge per time. Multiplying them gives energy per time.
Energy per charge
\[\Delta U=qV\]
Charge flow
\[I=\frac{\Delta q}{\Delta t}\]
Power
\[P=\frac{\Delta U}{\Delta t}=IV\]
Derivation 2: Resistor power forms
For an ohmic resistor, combine \(P=IV\) with \(V=IR\).
Start
\[P=IV\]
Substitute \(V=IR\)
\[P=I^2R\]
Substitute \(I=V/R\)
\[P=\frac{V^2}{R}\]
Derivation 3: Energy over time
If power is constant, total energy transferred is power multiplied by time.
Power definition
\[P=\frac{\Delta U}{\Delta t}\]
Constant power
\[\Delta U=P\Delta t\]
Rules
These are the compact power relations.
Power
\[P=IV\]
Resistor power
\[P=I^2R=\frac{V^2}{R}\]
Energy transfer
\[\Delta U=P\Delta t\quad\text{for constant power}\]
Watt
\[1\,\mathrm{W}=1\,\mathrm{J\,s^{-1}}\]
Examples
Question
A device has
\[12\,\mathrm{V}\]
across it and current \[2.0\,\mathrm{A}\]
Find the power.Answer
\[P=IV=(2.0)(12)=24\,\mathrm{W}\]
Checks
- \(P=IV\) uses the potential difference across the element carrying current \(I\).
- \(I^2R\) and \(V^2/R\) apply directly to ohmic resistors.
- Power is a rate; energy also needs a time interval.
- A passive resistor converts electrical energy into internal energy.