Voltage, Current, Power and Energy: the four quantities you'll never stop using
Why your electricity bill is in kWh and not in watts.
Students mix these four up constantly, and the confusion is understandable — everyday speech uses "power" and "energy" interchangeably. In engineering they are strictly different, and the difference is worth real marks. The cleanest way in is an analogy: think of water in a pipe.
💧 The water-pipe picture
VoltageThe pressure pushing water along. It's the energy given to each unit of charge — measured in volts (V), where 1 V = 1 joule per coulomb. Voltage is always measured between two points; "the voltage at a node" only means anything relative to a reference.
CurrentThe flow rate — how much water passes per second. It's charge per unit time, in amperes (A), where 1 A = 1 coulomb per second.
PowerThe rate at which energy is delivered — watts (W). One watt is one joule per second.
EnergyThe total amount delivered over time — joules (J), or kilowatt-hours for billing.
The definitions, precisely
P = V² / R With V = 12 V, R = 6 Ω, P = 24 W, I = 2 A.
Double the voltage and the power does not double — it quadruples. That square is why a small rise in supply voltage overheats a component that was comfortable before, and why resistor ratings are quoted in watts rather than volts.
Charge: Q = I × t (coulombs)
Current: I = Q / t (amperes = C/s)
Voltage: V = W / Q (volts = J/C)
Power: P = V × I = I²R = V²/R (watts = J/s)
Energy: E = P × t (joules, or watt-seconds)
Power is a rate; energy is a total. A 2000 W heater and a 40 W bulb can consume the same energy — the heater for 1 hour, the bulb for 50 hours. Your bill charges for energy (kWh), which is why leaving a low-power device on all month still costs something.
Worked numerical 1 — charge and current
A current of 3 A flows for 5 minutes. How much charge is transferred, and how many electrons is that?
t = 5 min = 300 s
Q = I × t = 3 × 300 = 900 C
Number of electrons = Q / e = 900 / (1.602 × 10⁻¹⁹)
= 5.62 × 10²¹ electrons
Note the unit conversion first — forgetting to turn minutes into seconds is the most common way this question is lost.
Worked numerical 2 — the electricity bill
A 2 kW immersion heater runs for 2.5 hours a day for 30 days. At NPR 10 per unit, what is the cost?
Energy per day = P × t = 2 kW × 2.5 h = 5 kWh
Energy per month = 5 × 30 = 150 kWh (150 "units")
Cost = 150 × 10 = NPR 1,500
In joules: 150 kWh × 3.6 × 10⁶ = 5.4 × 10⁸ J
One "unit" of electricity = 1 kilowatt-hour = 3.6 × 10⁶ joules. That conversion factor appears in nearly every energy-cost numerical, so commit it to memory.
Worked numerical 3 — combining with Ohm's law
A device draws 0.5 A from a 230 V supply. Find its resistance, power, and the energy used in 8 hours.
R = V/I = 230 / 0.5 = 460 Ω
P = V × I = 230 × 0.5 = 115 W
E = P × t = 115 × 8 = 920 Wh = 0.92 kWh
= 115 × (8 × 3600) = 3.312 × 10⁶ J
💡 Exam angle: definitions with units are frequently a 2–4 mark question on their own — write the unit and what it means (1 V = 1 J/C), not just the symbol. For numericals, the marks lost most often are unit conversions: minutes→seconds, kW→W, hours→seconds. Convert everything first, before substituting.
Syllabus points
Definitions and units
Power & energy calculations (numerical)
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