04 // Interactive Formula Compendium // PHYSICSV = I · R, P = V · I = I² R = V² / R
Ohm's Law, Joule Power & Kirchhoff's Circuit Laws (KCL / KVL) Sheet
Ohm's Law states that potential difference V across an ohmic conductor is proportional to current I times resistance R (V = IR), while Joule's Law gives electrical power dissipation P = VI = I²R = V²/R.
Formula Reference
Main Formula
V = I · R, P = V · I = I² R = V² / R
Rearranged Forms
Σ I_in = Σ I_out (Kirchhoff's Current Law / Node Charge Conservation)
Σ V_loop = 0 (Kirchhoff's Voltage Law / Loop Energy Conservation)
R_series = Σ R_i, 1 / R_parallel = Σ (1 / R_i)
Variables & Units
| Symbol | Name | Unit |
|---|---|---|
| V | Voltage Drop (V = I · R) | V |
| I | Electric Current (I) | A |
| R | Electrical Resistance (R) | Ω |
Inputs & Parameters
[A]
[Ω]
Calculated Result (Voltage Drop (V = I · R))
V =120V
Formula Notes & Background
- At the microscopic Drude level, current density J = σ E, which integrates across conductor length L and cross-section A to V = I · (ρL/A) = I R.
- Kirchhoff's Current Law (KCL) follows from conservation of electric charge (∇ · J = 0 in steady state at any node).
- Kirchhoff's Voltage Law (KVL) follows from electrostatic fields being conservative (∮ E · dl = 0 around any closed loop).
Step-by-Step Examples
#1: Find the required supply voltage and power dissipated by a 48 Ω heating element drawing 2.5 A.
I = 2.5 AR = 48 Ω
V = 2.5 × 48 = 120 V; P = (2.5)² × 48 = 6.25 × 48
→ V = 120 V, Power P = 300 W
#2: Find the equivalent resistance of R₁ = 60 Ω and R₂ = 30 Ω wired in parallel.
R₁ = 60 ΩR₂ = 30 Ω
R_eq = (R₁ × R₂) / (R₁ + R₂) = 1800 / 90
→ R_eq = 20 Ω
Was this tool helpful?
Frequently Asked Questions
Why do high-voltage transmission lines step voltage up to hundreds of kilovolts?+
To transmit fixed power P = VI, raising V reduces line current I = P/V proportionally, which slashes resistive line heat loss P_loss = I²R_line by the square of the voltage factor.
How does wire resistance depend on length L and cross-sectional area A?+
By Pouillet's Law, R = ρ L / A, where ρ is the material's electrical resistivity (e.g. 1.68 × 10⁻⁸ Ω·m for copper).
What is the voltage divider formula for two series resistors?+
Across resistor R₂ in series with R₁ across source V_in, the output voltage is V_out = V_in × R₂ / (R₁ + R₂).