Ohm's law and the power formulas
Ohm's law states that the current through an ohmic conductor is proportional to the voltage across it: V = I × R. Combined with P = V × I, any two of voltage, current, resistance and power determine the other two.
| Find | From V and I | From I and R | From V and R | From P and one other |
|---|---|---|---|---|
| Voltage V | — | V = I·R | — | V = P/I = √(P·R) |
| Current I | — | — | I = V/R | I = P/V = √(P/R) |
| Resistance R | R = V/I | — | — | R = V²/P = P/I² |
| Power P | P = V·I | P = I²·R | P = V²/R | — |
Sources: OpenStax: University Physics Volume 2, 9.4 Ohm's Law; OpenStax: University Physics Volume 2, 9.5 Electrical Energy and Power
Kirchhoff's laws
Kirchhoff's current law (the junction rule) says the sum of currents entering a node equals the sum leaving it: ΣI_in = ΣI_out, or ΣI = 0 with signs. It follows from conservation of charge.
Kirchhoff's voltage law (the loop rule) says the algebraic sum of voltage changes around any closed loop is zero: ΣV = 0. It follows from conservation of energy. Voltage rises across sources and drops across resistors (by I·R in the direction of current).
- Series circuit: the same current flows through every part, and the source voltage equals the sum of the drops.
- Parallel circuit: every branch has the same voltage, and the source current equals the sum of the branch currents.
Sources: OpenStax: University Physics Volume 2, 10.3 Kirchhoff's Rules
Voltage divider rule
Two resistors in series across a supply V_in divide it in proportion to their resistance. The voltage across R₂ is V_out = V_in × R₂ / (R₁ + R₂). This holds when the output is unloaded; a load across R₂ acts in parallel with it and lowers V_out.
| V_in | R₁ | R₂ | V_out |
|---|---|---|---|
| 5 V | 10 kΩ | 10 kΩ | 2.5 V |
| 12 V | 10 kΩ | 4.7 kΩ | 3.837 V |
| 9 V | 1 kΩ | 2 kΩ | 6 V |
| 3.3 V | 4.7 kΩ | 10 kΩ | 2.245 V |
| 24 V | 100 kΩ | 10 kΩ | 2.182 V |
Sources: OpenStax: University Physics Volume 2, 10.2 Resistors in Series and Parallel
Coulomb's law
The force between two point charges is F = k·|q₁·q₂| / r², directed along the line joining them: repulsive for like charges and attractive for opposite charges. The constant is k = 1/(4πε₀) ≈ 8.987552 × 10⁹ N·m²/C², where ε₀ = 8.8541878188 × 10⁻¹² F/m is the CODATA 2022 value of the vacuum electric permittivity.
| q₁ | q₂ | Distance r | Force F |
|---|---|---|---|
| 1 C | 1 C | 1 m | 8.9876 × 10⁹ N |
| 1 µC | 1 µC | 1 m | 8.9876 × 10⁻³ N |
| 1 µC | −2 µC | 10 cm | 1.7975 N (attractive) |
| e | e | 1 nm | 2.3071 × 10⁻¹⁰ N |
Sources: OpenStax: University Physics Volume 2, 5.3 Coulomb's Law; NIST: CODATA Value: vacuum electric permittivity