Topic 11.1111 min read
Electrical Power
Electrical power is the rate of electrical energy transfer.
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Power tells how quickly energy changes form. A higher-power lamp converts more electrical energy each second than a lower-power lamp operating for the same time.
One watt means one joule of energy is transferred every second.
Recommended for Class 11
Electrical power is the rate at which a circuit transfers electrical energy into heat, light, sound, motion or another form. It connects the energy-per-charge meaning of voltage with the charge-per-time meaning of current.
Deriving P=VI
Multiplying energy per coulomb by coulombs per second gives energy per second.
- P
- power transferred (W)
- V
- potential difference (V)
- I
- current (A)
This relationship is general for a circuit element when V and I refer to that same element and the signs are interpreted consistently.
Power in a resistor
For an ohmic resistor, substitute V=IR into P=VI.
Alternatively substitute I=VR.
Why current heats a resistor
An electric field gives energy to mobile electrons. Their collisions transfer this energy to the lattice, increasing the material's thermal energy. The heating rate is I²R.
At fixed resistance, doubling current makes heating power four times larger because power depends on I².
| Fixed condition | Power relation | Consequence |
|---|---|---|
| R fixed | P=I²R | Doubling I makes P four times larger |
| V fixed | P=V²R | Increasing R reduces power |
| I fixed | P=I²R | Increasing R increases power |
Electrical energy
The joule is the SI energy unit. When power varies, total energy is found from the area under a power-time graph or by summing energy over intervals.
Kilowatt-hour
Electricity suppliers use the kilowatt-hour, a unit of energy. It is the energy used by a 1 kW appliance operating for 1 h.
Appliance ratings
A label such as 230 V, 1000 W means the appliance is designed to use 1000 J each second when connected to 230 V. Its operating current follows from I=PV.
Using an appliance at a voltage different from its rating can change its power and may prevent correct operation or cause damage.
Efficiency
A device may not convert all input electrical power into the desired output form. Efficiency compares useful output with total input.
Worked example 1
A 12 V device draws 2.0 A for 5.0 min.
Worked example 2
A 2.0 kW heater operates for 3.0 h.
Exam-ready method
- Identify whether the question asks for power or energy.
- Start with P=VI; use Ohm's law only when appropriate.
- Choose I²R when current and resistance are known, or V²R when voltage and resistance are known.
- Convert minutes to seconds for joules.
- Use kilowatts and hours together for kilowatt-hours.
- State what remains fixed before reasoning about resistance and power.
Exam Focus
Exam Focus
Important points
- Power definition
- P=VI derivation
- Resistor power forms
- Watt
- Electrical energy
- Kilowatt-hour
- Ratings
- Fixed-variable reasoning
Important formulas
- P=VI
- P=I2R
- P=V2R
- W=Pt
- 1\ \mathrm{kWh}=3.6\times10^6\ \mathrm{J}
Common exam traps
- Convert time correctly.
- Distinguish energy from power.
Long question structure
Energy rate → derive P=VI → resistor forms → heating → energy units → ratings → examples
Common Mistakes
Common Mistakes
- Mistake
Confusing power with energy.
- Mistake
Calling kilowatt-hour a unit of power.
- Mistake
Using P=I²R or V²R without an ohmic-resistor relation.
- Mistake
Failing to convert minutes to seconds for joules.
- Mistake
Claiming power always increases with resistance without stating what remains fixed.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
The general circuit relation is P=VI.
For an ohmic resistor, P=I²R=V²R.
One watt equals one joule per second.
Electrical energy is W=Pt=VIt.
Electrical power is the rate of electrical energy transfer.
P=VI=I2R=V2R, W=Pt
- Definition
- Electrical power is the rate of electrical energy transfer.
- Formula
- P=VI=I2R=V2R, W=Pt
- Example
- A 12 V, 2.0 A device uses 24 W and 7.2×10³ J in 5.0 min.
- Critical warning
- Kilowatt-hour is energy; kilowatt is power.
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Exam Practice
Definition
Q1. Define electrical power and state its SI unit.
Derivation
Q2. Derive P=VI.
Formula
Q3. Derive the resistor power forms.
Numerical
Q4. A 12 V device draws 2.0 A for 5.0 min. Find power and energy.
Reasoning
Q5. Why must the fixed quantity be stated when discussing resistance and power?