Electric Work

Calculate electrical work/energy using voltage, current, and time.

Inputs

U

I

t

Formula Interpretation

Electric Work

W = U I t

$W$ (J) is electrical energy, equal to voltage $U$ (V) × current $I$ (A) × time $t$ (s). Physically, the source does work on charge to convert chemical or mechanical energy into electrical energy, which the load then converts to heat, mechanical work, or light. For non-constant power, total energy requires integration: $W = \int_0^t P(\tau)\,\mathrm{d}\tau$ .

Electrical Power

P = U I

Power $P$ (W) = $U$ × $I$ is the instantaneous rate of energy transfer (1 W = 1 J/s). Power determines peak load requirements that size conductors and breakers; energy (work) is power integrated over time and determines the resources consumed and electricity bill. Both must be considered in system design.

Work in Wh

W_{\text{Wh}} = U I \cdot \dfrac{t}{3600}

1 Wh = 3600 J; divide $W_{\text{Wh}}$ (J) by 3600 to obtain watt-hours. Wh and kWh are the standard units for electricity billing and battery capacity. For example, a 100 W bulb running for 10 hours consumes 1 kWh (one unit of electricity).

Work in kWh

W_{\text{kWh}} = \dfrac{W_{\text{Wh}}}{1000}

1 kWh = 1000 Wh = 3.6 × 10⁶ J — the billing unit shown on electricity meters. Industrial energy accounting often uses MWh (1 MWh = 1000 kWh) or GWh for generation statistics. Dividing $W_{\text{Wh}}$ by 1000 gives $W_{\text{kWh}}$ .

Knowledge Points

Power vs. energy — the key distinction

Power $P$ (W) is the rate of energy transfer; electric work $W = Pt$ (J) is energy accumulated over time. A 2000 W kettle running for 30 minutes consumes $W = 2000 \times 1800 = 3.6 \times 10^6$ J = 1 kWh. A 5 W device in standby for a full year consumes about $5 \times 8760 / 1000 \approx 44$ kWh — far more than most people expect. Energy optimisation must consider both power level and usage duration.

Energy unit conversion hierarchy

1 kWh = 3.6 MJ = 3.6×10⁶ J; 1 MWh = 1000 kWh; 1 GWh = 10⁶ kWh. Other common energy units: 1 kcal ≈ 4.186 kJ (food and heating); 1 BTU ≈ 1055 J (North American HVAC). Electricity bills use kWh; utility-scale generation uses GWh and TWh. Being able to convert between units is essential for comparing energy technologies and costs.

Appliance energy audit and annual cost estimation

Annual energy use: $W_{\text{annual}} = P \times t_{\text{annual}}$ (kWh); annual cost ≈ $W_{\text{annual}} \times$ tariff (£/kWh or $/kWh). For example, a 1.5 kW air conditioner running 8 hours/day for 120 days consumes$ 1.5 \times 8 \times 120 = 1440$ kWh per year. At a tariff of £0.30/kWh this costs £432. Energy-efficiency labels (A+++ to G in the EU, or ENERGY STAR in the USA) help identify equipment that delivers the same output with significantly lower electricity consumption.

Energy efficiency ratio (EER/COP) and savings evaluation

The Energy Efficiency Ratio (EER) or Coefficient of Performance (COP) is the ratio of useful energy output to electrical energy input. Air conditioners typically achieve a COP of 2.5–5 (consuming 1 kWh of electricity delivers 2.5–5 kWh of cooling); heat-pump water heaters reach COP 3–5, far superior to direct-resistance heaters (COP = 1 by definition). Selecting high-COP equipment is the most direct way to reduce electricity consumption and carbon emissions for a given service output. LED lamps consume about 80% less power than incandescent bulbs for equivalent luminous flux.

Example

A fan rated at $P = 100\,\text{W}$ runs for $t = 2\,\text{h}$ . Find energy use $W = 0.2\,\text{kWh}$ and estimate cost.

Step 1 — Compute kWh

W_{\text{kWh}} = \dfrac{100 \times 2}{1000} = 0.2\,\text{kWh}

Step 2 — Compute cost

C = 0.2 \times 0.6 = 0.12\,\text{元}

Therefore the energy is $W = 0.2\,\text{kWh}$ and the cost is $0.12\,\text{元}$ .

Extended Knowledge

•Integrating variable power and reactive power：For time-varying power, total energy is $W = \int_0^t P(\tau)\,\mathrm{d}\tau = \int_0^t U(\tau)I(\tau)\,\mathrm{d}\tau$ . In AC circuits, active (real) power is $P_{\text{active}} = U_{\text{rms}} I_{\text{rms}} \cos\varphi$ (W), apparent power is $S = U_{\text{rms}} I_{\text{rms}}$ (VA), and reactive power $Q = S \sin\varphi$ (var). Electricity meters record active energy (kWh); industrial customers also pay reactive-power penalties and install capacitor banks to improve power factor and reduce demand charges.
•Standby (vampire) power losses：Devices in standby or soft-off states continuously draw small amounts of power — the so-called vampire or phantom load. Typical standby figures: router 5–10 W, set-top box 10–20 W, idling computer monitor 1–5 W, microwave clock 2–3 W. Globally, standby losses account for an estimated 5–10% of total residential electricity consumption. Smart plugs with timers, one-touch master switches, and zero-standby-power product designs are practical countermeasures.
•Carbon footprint and grid emission factor：The CO₂ emitted per kWh of electricity consumed depends on the grid emission factor (kgCO₂/kWh), which varies widely by country and energy mix. Representative values: France (mainly nuclear) ≈ 0.05, Norway (mainly hydro) ≈ 0.02, UK ≈ 0.23, Germany ≈ 0.40, Australia (coal-heavy) ≈ 0.65, China national average ≈ 0.58. Multiplying electricity consumption (kWh) by the local emission factor converts energy use into a carbon footprint for ESG reporting, environmental product declarations, and personal climate action.
•Time-of-use pricing and demand-side management：Time-of-use (TOU) tariffs split the day into peak, shoulder, and off-peak periods with different unit prices, incentivising consumers to shift flexible loads (dishwashers, EV charging, water heating) to low-price overnight periods. Smart meters and Home Energy Management Systems (HEMS) can automate this shift. Industrial customers face demand charges based on peak 15-minute or 30-minute demand (kW), so flattening the load profile — through battery storage, load scheduling, or demand-response contracts — directly reduces the electricity bill''s fixed component.

Electric Work

Calculate electrical work/energy using voltage, current, and time.

Inputs

U

I

t

Formula Interpretation

Electric Work

W = U I t

Electrical Power

P = U I

Work in Wh

W_{\text{Wh}} = U I \cdot \dfrac{t}{3600}

Work in kWh

W_{\text{kWh}} = \dfrac{W_{\text{Wh}}}{1000}

Knowledge Points

Power vs. energy — the key distinction

Energy unit conversion hierarchy

Appliance energy audit and annual cost estimation

Energy efficiency ratio (EER/COP) and savings evaluation

Example

A fan rated at $P = 100\,\text{W}$ runs for $t = 2\,\text{h}$ . Find energy use $W = 0.2\,\text{kWh}$ and estimate cost.

Step 1 — Compute kWh

W_{\text{kWh}} = \dfrac{100 \times 2}{1000} = 0.2\,\text{kWh}

Step 2 — Compute cost

C = 0.2 \times 0.6 = 0.12\,\text{元}

Therefore the energy is $W = 0.2\,\text{kWh}$ and the cost is $0.12\,\text{元}$ .

Extended Knowledge

•Integrating variable power and reactive power：For time-varying power, total energy is $W = \int_0^t P(\tau)\,\mathrm{d}\tau = \int_0^t U(\tau)I(\tau)\,\mathrm{d}\tau$ . In AC circuits, active (real) power is $P_{\text{active}} = U_{\text{rms}} I_{\text{rms}} \cos\varphi$ (W), apparent power is $S = U_{\text{rms}} I_{\text{rms}}$ (VA), and reactive power $Q = S \sin\varphi$ (var). Electricity meters record active energy (kWh); industrial customers also pay reactive-power penalties and install capacitor banks to improve power factor and reduce demand charges.
•Standby (vampire) power losses：Devices in standby or soft-off states continuously draw small amounts of power — the so-called vampire or phantom load. Typical standby figures: router 5–10 W, set-top box 10–20 W, idling computer monitor 1–5 W, microwave clock 2–3 W. Globally, standby losses account for an estimated 5–10% of total residential electricity consumption. Smart plugs with timers, one-touch master switches, and zero-standby-power product designs are practical countermeasures.
•Carbon footprint and grid emission factor：The CO₂ emitted per kWh of electricity consumed depends on the grid emission factor (kgCO₂/kWh), which varies widely by country and energy mix. Representative values: France (mainly nuclear) ≈ 0.05, Norway (mainly hydro) ≈ 0.02, UK ≈ 0.23, Germany ≈ 0.40, Australia (coal-heavy) ≈ 0.65, China national average ≈ 0.58. Multiplying electricity consumption (kWh) by the local emission factor converts energy use into a carbon footprint for ESG reporting, environmental product declarations, and personal climate action.
•Time-of-use pricing and demand-side management：Time-of-use (TOU) tariffs split the day into peak, shoulder, and off-peak periods with different unit prices, incentivising consumers to shift flexible loads (dishwashers, EV charging, water heating) to low-price overnight periods. Smart meters and Home Energy Management Systems (HEMS) can automate this shift. Industrial customers face demand charges based on peak 15-minute or 30-minute demand (kW), so flattening the load profile — through battery storage, load scheduling, or demand-response contracts — directly reduces the electricity bill''s fixed component.