Electricity Formulas

Every circuit, from a flashlight to a phone charger, follows a handful of rules about voltage, current and resistance. Learn these and you can read a power bill, size a resistor for an LED and see why a capacitor takes time to charge.

7 formulas, in the order that makes them easiest to learn:

Ohm's Law

$$V = I R$$

Ohm’s law says the push on a wire, the voltage, equals the flow through it, the current, times how hard that flow is to get through, the resistance.

Electric Power

$$P = V I$$

Electric power tells you how fast a device uses energy, and you get it by multiplying the volts by the amps to get watts.

Energy and Kilowatt-Hours

$$E = P \, t$$

Energy is power multiplied by time, so a heater that uses 2 kilowatts for 3 hours uses 6 kilowatt-hours of energy.

Resistors in Series and Parallel

$$R_{\text{series}} = R_1 + R_2 + \cdots + R_n \qquad \frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$$

Resistors in a line add up, and resistors side by side always give a total smaller than the smallest one.

Kirchhoff's Current Law

$$\sum I_{\text{in}} = \sum I_{\text{out}}$$

Kirchhoff’s current law says that whatever electricity flows into a junction has to flow out again, because nothing piles up there.

RC Time Constant

$$\tau = R C$$

The RC time constant tells you how long a capacitor takes to fill up through a resistor: multiply the resistance by the capacitance.

Coulomb's Law

$$F = k_e \frac{|q_1 q_2|}{r^2}$$

Coulomb’s law tells you how hard two electric charges push or pull each other, and the force gets weaker fast as they move apart.

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