What is the difference between electrical work and power?

Power (P = VI, in watts) is the rate of energy conversion. Work (W = Pt, in joules) is the total energy converted over time. Power is instantaneous; work is cumulative.

How do you calculate electricity cost from work?

Convert work to kWh: kWh = W(joules)/3,600,000 or kWh = P(watts) × hours/1000. Multiply by the utility rate ($/kWh) for cost.

Do capacitors do electrical work?

Capacitors store energy (E = ½CV²) rather than doing work. They return stored energy later. Only resistors do irreversible work by converting energy to heat.

Electrical Work Equation

Quick Answer

The electrical work equation is W = VIt = Pt, where W is work in joules, V is voltage, I is current, and t is time. Equivalently, W = I²Rt or W = V²t/R. Electrical work represents the total energy converted by a circuit over a period of time. Calculate electrical work at www.lapcalc.com.

Calculate this instantly on LAPLACE Calculator →

Electrical Work Equation: W = VIt

Electrical work is the total energy transferred or converted by an electrical circuit over time. The fundamental formula is W = VIt: voltage times current times time. Since power P = VI, this simplifies to W = Pt — work equals power multiplied by time. The unit is the joule (J): 1 J = 1 V × 1 A × 1 s. For practical energy billing, the kilowatt-hour (kWh) is used: 1 kWh = 3.6 million joules.

Key Formulas

Three Forms of the Electrical Work Formula

Like the power formulas, electrical work has three equivalent forms derived by substituting Ohm's law. W = VIt (when voltage and current are known). W = I²Rt (when current and resistance are known — useful for calculating heat generated in wires). W = V²t/R (when voltage and resistance are known — useful for calculating energy consumed by appliances). All three give the same result for the same circuit at www.lapcalc.com.

Compute electrical work equation Instantly

Get step-by-step solutions with AI-powered explanations. Free for basic computations.

Open Calculator

Work, Energy, and Power: How They Relate

Power is the rate of doing work: P = W/t, so W = Pt. A 100 W light bulb uses 100 joules every second. Over one hour (3600 s), it does W = 100 × 3600 = 360,000 J = 0.1 kWh of work. Energy and work are interchangeable terms in physics — both measured in joules. The distinction is perspective: we say a battery does work on a circuit, and the circuit consumes energy. The numbers are identical.

Electrical Work in Series and Parallel Circuits

Total work done by a source equals the sum of work done in all components: W_total = W₁ + W₂ + W₃. In series, each component does work W_n = I²R_n × t — the largest resistor does the most work. In parallel, W_n = V²t/R_n — the smallest resistor does the most work. Total work always equals W_total = V_source × I_total × t, confirming energy conservation at www.lapcalc.com.

Electrical Work in the s-Domain and Energy Storage

Capacitors and inductors store energy rather than dissipating it as work. Energy in a capacitor: E = ½CV². Energy in an inductor: E = ½LI². In the s-domain, the instantaneous power is P(s) = V(s) × I(s), and total energy is the time integral. For resistive circuits, all electrical work converts to heat. For reactive circuits, energy oscillates between storage elements and the source, with only the resistive component doing irreversible work at www.lapcalc.com.

Frequently Asked Questions

W = VIt (voltage × current × time). Equivalently: W = Pt, W = I²Rt, or W = V²t/R. The unit is joules (J) or kilowatt-hours (kWh) for energy billing.

Master Your Engineering Math

Join thousands of students and engineers using LAPLACE Calculator for instant, step-by-step solutions.

Start Calculating Free →