Electrical Energy and Power

DC Circuits · 10 min read

Your phone charger, a laptop, a kettle, and a toaster all move energy — but at very different speeds. The rate at which a circuit moves energy is called power, and it is what every fuse, battery, and heat sink is designed around.

Understanding power lets you answer questions like: Why does a short circuit blow a fuse instantly? Why do transmission lines run at high voltage? How long will a battery last?

Power in Everyday Life

These are typical power ratings for common devices:

Device	Power
LED bulb	6 W
USB charger	20 W
Laptop	65 W
Toaster	1 500 W
Kettle	2 300 W

The kettle moves energy nearly 400× faster than an LED bulb — both at the same mains voltage.

What Power Means

Power is energy per unit time: $P = E / t$ . In an electrical circuit:

P = V \cdot I

Voltage times current, measured in watts (W). One watt = one joule per second. Everything a circuit does — heat, light, motion, sound — is an energy conversion at a rate set by $P = VI$ .

The Three Forms

Combine $P = VI$ with Ohm's Law and you get three equivalent expressions:

P = V \cdot I \qquad P = I^{2} R \qquad P = \dfrac{V^{2}}{R}

Know V and I? → Use $P = V I$
Know I and R? → Use $P = I^{2} R$
Know V and R? → Use $P = V^{2} / R$

= V × I

= P ∕ I

= P ∕ V

Figure 1. The power triangle — cover the unknown; the remaining two letters show the formula. P on top; V and I side by side.

Worked Example

A 12 V battery drives current through a 3 Ω resistor. What power does the resistor dissipate?

Find current first: $I = V / R = 12 / 3 = 4 \text{ A}$
Choose power form — know V and I, so use $P = V I$
Substitute: $P = 12 \times 4$
Answer: P = 48 W

Result:

48 \text{ W}

— enough to feel warm to the touch. Verify with

P = V^{2}/R = 144/3 = 48 \text{ W}

✓

The Squared Relationships

Power does not scale linearly with voltage or current — it scales with the square.

Energy = Power × Time

Energy is power sustained over time: $E = P \cdot t$ . In SI units that is joules; on an electricity bill it is kilowatt-hours (kWh).

A 60 W bulb left on for 10 hours uses 0.6 kWh — roughly the cost of a coffee at UK prices.

Think Before Calculating

Predict the outcome first — then verify with the power equations.

Scenario 1: A 12-volt source drives 2 A through a resistor. You double the voltage to 24 V (same resistor). What happens to the power?

Scenario 2: A resistor dissipates 10 W. You double its resistance (same voltage supply). What happens to power?

Scenario 3: A 100 W device runs for 5 hours. How much energy is used, and what does it cost at £0.28 per kWh?

Common Mistakes

Power Playground

Explore how power changes with resistance, or calculate the energy cost of any device.

Voltage12.0 V

1 V24 V

Resistance100 Ω

1 Ω1 kΩ

Power (P = V²/R)

1.44 W

Current (I = V/R)

120.00 mA

P vs R — V = 12.0 V (log scale)

✅ Power = rate of energy transfer, measured in watts (W)
✅ Three forms: $P = VI$ , $P = I^{2}R$ , $P = V^{2}/R$
✅ Doubling voltage quadruples power (squared relationship)
✅ Doubling current quadruples power (squared relationship)
✅ Energy = Power × Time: $E = P \cdot t$
✅ Electricity bills use kilowatt-hours (kWh), not watts