# Electricity Formulas

Every circuit, from a flashlight to a power grid, follows a short list of rules about voltage, current and resistance, and a few more about capacitors, coils and magnets. Learn these and you can read a power bill, size a resistor for an LED, see why a capacitor takes time to charge and why a transformer only works on AC.

Page: https://formulabro.yunusemrevurgun.com/electricity/  
Updated: 2026-10-22

## [Ohm's Law](https://formulabro.yunusemrevurgun.com/electricity/ohms-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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/ohms-law.md

## [Electric Power](https://formulabro.yunusemrevurgun.com/electricity/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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/electric-power.md

## [Energy and Kilowatt-Hours](https://formulabro.yunusemrevurgun.com/electricity/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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/energy-and-kilowatt-hours.md

## [Resistors in Series and Parallel](https://formulabro.yunusemrevurgun.com/electricity/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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/resistors-in-series-and-parallel.md

## [Kirchhoff's Current Law](https://formulabro.yunusemrevurgun.com/electricity/kirchhoffs-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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/kirchhoffs-current-law.md

## [RC Time Constant](https://formulabro.yunusemrevurgun.com/electricity/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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/rc-time-constant.md

## [Coulomb's Law](https://formulabro.yunusemrevurgun.com/electricity/coulombs-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.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/coulombs-law.md

## [Charge and Current](https://formulabro.yunusemrevurgun.com/electricity/charge-and-current/)

$$
I = \frac{Q}{t}
$$

Electric current is how much charge passes a point each second, so the same charge moving faster means more current.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/charge-and-current.md

## [Kirchhoff's Voltage Law](https://formulabro.yunusemrevurgun.com/electricity/kirchhoffs-voltage-law/)

$$
\sum_{k} V_k = 0
$$

Kirchhoff's voltage law says that if you walk all the way around a circuit loop, the voltage gained equals the voltage lost.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/kirchhoffs-voltage-law.md

## [Voltage Divider](https://formulabro.yunusemrevurgun.com/electricity/voltage-divider/)

$$
V_{\text{out}} = V_{\text{in}} \frac{R_2}{R_1 + R_2}
$$

A voltage divider uses two resistors in series to take a smaller share of a supply voltage, with the share set by their ratio.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/voltage-divider.md

## [Current Divider](https://formulabro.yunusemrevurgun.com/electricity/current-divider/)

$$
I_1 = I_{\text{total}} \frac{R_2}{R_1 + R_2}
$$

A current divider splits a total current between two parallel resistors, and the smaller resistor always takes the bigger share.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/current-divider.md

## [Resistivity](https://formulabro.yunusemrevurgun.com/electricity/resistivity/)

$$
R = \rho \frac{L}{A}
$$

A wire's resistance grows with its length, shrinks with its thickness, and depends on what the wire is made of.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/resistivity.md

## [Temperature Coefficient of Resistance](https://formulabro.yunusemrevurgun.com/electricity/temperature-coefficient-of-resistance/)

$$
R = R_0\left[1 + \alpha (T - T_0)\right]
$$

Most metals get harder to push current through as they get hotter, and this formula estimates how much the resistance rises.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/temperature-coefficient-of-resistance.md

## [Drift Velocity](https://formulabro.yunusemrevurgun.com/electricity/drift-velocity/)

$$
v_d = \frac{I}{n q A}
$$

Electrons in a copper wire drift along at a fraction of a millimetre per second, even though the electric signal races along the wire.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/drift-velocity.md

## [Internal Resistance](https://formulabro.yunusemrevurgun.com/electricity/internal-resistance/)

$$
V = \varepsilon - I r
$$

A real battery has a small resistance inside it, so its output voltage drops when it pushes a current through a load.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/internal-resistance.md

## [Maximum Power Transfer](https://formulabro.yunusemrevurgun.com/electricity/maximum-power-transfer/)

$$
R_L = R_S \qquad P_{\max} = \frac{V_S^2}{4 R_S}
$$

A load receives the most power when its resistance matches the source's resistance, but then half the power is lost inside the source.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/maximum-power-transfer.md

## [Wheatstone Bridge](https://formulabro.yunusemrevurgun.com/electricity/wheatstone-bridge/)

$$
\frac{R_1}{R_2} = \frac{R_3}{R_x}
$$

A Wheatstone bridge finds an unknown resistance by adjusting a known one until the meter between two midpoints reads zero, then doing one multiply and one divide.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/wheatstone-bridge.md

## [Battery Capacity and Runtime](https://formulabro.yunusemrevurgun.com/electricity/battery-capacity-runtime/)

$$
t = \frac{C}{I}
$$

Divide a battery's capacity by the current the device draws, and you get roughly how many hours the battery will run it.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/battery-capacity-runtime.md

## [Capacitance](https://formulabro.yunusemrevurgun.com/electricity/capacitance/)

$$
Q = C V
$$

Capacitance tells you how much electric charge a capacitor stores for each volt across it.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/capacitance.md

## [Parallel-Plate Capacitor](https://formulabro.yunusemrevurgun.com/electricity/parallel-plate-capacitor/)

$$
C = \frac{\varepsilon_0 \varepsilon_r A}{d}
$$

The parallel-plate formula says a capacitor holds more charge per volt when its plates are bigger, closer together, or separated by a material with a higher permittivity.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/parallel-plate-capacitor.md

## [Capacitors in Series and Parallel](https://formulabro.yunusemrevurgun.com/electricity/capacitors-in-series-and-parallel/)

$$
C_{\text{par}} = C_1 + C_2 + \cdots \qquad \frac{1}{C_{\text{ser}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots
$$

Capacitors side by side add their capacitance, while capacitors chained end to end give a smaller total that is found with reciprocals.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/capacitors-in-series-and-parallel.md

## [Energy Stored in a Capacitor](https://formulabro.yunusemrevurgun.com/electricity/energy-stored-in-capacitor/)

$$
E = \frac{1}{2} C V^2
$$

A charged capacitor stores energy in the electric field between its plates, and the amount grows with the square of the voltage.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/energy-stored-in-capacitor.md

## [Inductor Voltage](https://formulabro.yunusemrevurgun.com/electricity/inductor-voltage/)

$$
V = L \frac{dI}{dt}
$$

An inductor pushes back against changes in current, and the voltage across it is set by how fast the current is changing.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/inductor-voltage.md

## [Energy Stored in an Inductor](https://formulabro.yunusemrevurgun.com/electricity/energy-stored-in-inductor/)

$$
E = \frac{1}{2} L I^2
$$

A coil with current flowing through it stores energy in its magnetic field, and the amount grows with the square of the current.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/energy-stored-in-inductor.md

## [RL Time Constant](https://formulabro.yunusemrevurgun.com/electricity/rl-time-constant/)

$$
\tau = \frac{L}{R}
$$

The RL time constant tells you how long current takes to build up in a coil connected through a resistor: divide the inductance by the resistance.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/rl-time-constant.md

## [Capacitive Reactance](https://formulabro.yunusemrevurgun.com/electricity/capacitive-reactance/)

$$
X_C = \frac{1}{2\pi f C}
$$

Capacitive reactance tells you how hard a capacitor pushes back against alternating current, and it gets smaller as the frequency goes up.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/capacitive-reactance.md

## [Inductive Reactance](https://formulabro.yunusemrevurgun.com/electricity/inductive-reactance/)

$$
X_L = 2\pi f L
$$

Inductive reactance tells you how hard a coil pushes back against alternating current, and it gets bigger as the frequency goes up.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/inductive-reactance.md

## [Series RLC Impedance](https://formulabro.yunusemrevurgun.com/electricity/rlc-impedance/)

$$
Z = \sqrt{R^2 + (X_L - X_C)^2}
$$

Impedance is the total opposition a series circuit of a resistor, a coil and a capacitor gives to alternating current.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/rlc-impedance.md

## [Resonant Frequency](https://formulabro.yunusemrevurgun.com/electricity/resonant-frequency/)

$$
f_0 = \frac{1}{2\pi\sqrt{LC}}
$$

The resonant frequency is the one frequency where a coil and a capacitor trade energy back and forth most easily, and radios use it to tune in stations.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/resonant-frequency.md

## [RMS Voltage](https://formulabro.yunusemrevurgun.com/electricity/rms-voltage/)

$$
V_{\text{rms}} = \frac{V_{\text{peak}}}{\sqrt{2}}
$$

RMS voltage is the steady voltage that heats a resistor as much as an AC sine wave does, and you get it by dividing the peak voltage by the square root of 2.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/rms-voltage.md

## [AC Power Factor](https://formulabro.yunusemrevurgun.com/electricity/ac-power-factor/)

$$
P = V_{\text{rms}} I_{\text{rms}} \cos\varphi
$$

Power factor tells you what share of the current in an AC circuit does useful work, and it is the ratio of real power to apparent power.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/ac-power-factor.md

## [Three-Phase Power](https://formulabro.yunusemrevurgun.com/electricity/three-phase-power/)

$$
P = \sqrt{3}\, V_L I_L \cos\varphi
$$

Three-phase power tells you how much real power a balanced three-wire AC load uses, and you get it from the line voltage, the line current and the power factor.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/three-phase-power.md

## [Transformer Turns Ratio](https://formulabro.yunusemrevurgun.com/electricity/transformer-turns-ratio/)

$$
\frac{V_s}{V_p} = \frac{N_s}{N_p}
$$

A transformer changes an AC voltage up or down in the same ratio as the number of wire turns on its two coils.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/transformer-turns-ratio.md

## [Electric Field of a Point Charge](https://formulabro.yunusemrevurgun.com/electricity/electric-field-of-point-charge/)

$$
E = \frac{k_e\, q}{r^2}
$$

The electric field around a charge tells you the push that a small test charge would feel at each point in space.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/electric-field-of-point-charge.md

## [Electric Potential](https://formulabro.yunusemrevurgun.com/electricity/electric-potential/)

$$
V = \frac{k_e\, q}{r}
$$

Electric potential tells you how much energy each unit of charge would have at a spot in space, measured in volts.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/electric-potential.md

## [Magnetic Force on a Moving Charge](https://formulabro.yunusemrevurgun.com/electricity/magnetic-force-on-moving-charge/)

$$
F = |q|\, v\, B \sin\theta
$$

A magnetic field pushes a moving charge sideways, and the push is biggest when the charge moves straight across the field lines.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/magnetic-force-on-moving-charge.md

## [Force on a Current-Carrying Wire](https://formulabro.yunusemrevurgun.com/electricity/force-on-current-carrying-wire/)

$$
F = B\, I\, L \sin\theta
$$

A wire carrying current is pushed sideways by a magnetic field, and the push grows with the current, the wire length and the field strength.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/force-on-current-carrying-wire.md

## [Magnetic Field of a Straight Wire](https://formulabro.yunusemrevurgun.com/electricity/magnetic-field-of-straight-wire/)

$$
B = \frac{\mu_0 I}{2\pi r}
$$

A current in a straight wire makes a magnetic field that wraps around the wire, and the field gets weaker the farther away you measure it.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/magnetic-field-of-straight-wire.md

## [Magnetic Field of a Solenoid](https://formulabro.yunusemrevurgun.com/electricity/magnetic-field-of-solenoid/)

$$
B = \mu_0\, n\, I
$$

A long coil of wire makes a strong, nearly uniform magnetic field along its middle, and the field depends on how many turns are packed into each meter.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/magnetic-field-of-solenoid.md

## [Faraday's Law of Induction](https://formulabro.yunusemrevurgun.com/electricity/faradays-law/)

$$
\varepsilon = -N\, \frac{d\Phi_B}{dt}
$$

A changing magnetic field through a loop of wire pushes a voltage into the wire, and that is how generators make electricity.

Markdown: https://formulabro.yunusemrevurgun.com/electricity/faradays-law.md