Ohm's Law: The Foundation of Circuit Analysis
Ohm's Law states that voltage equals current times resistance. Combined with the power formula, all four electrical quantities can be calculated from any two known values.
The Four Formulas
V = I × R (Voltage)
I = V / R (Current)
R = V / I (Resistance)
P = V × I (Power)
Also: P = I²R = V²/RWorked Examples
LED circuit: V=5V, R=220Ω
I = 5/220 = 22.7 mA ✓ (safe for most LEDs)
P = 5 × 0.0227 = 0.114 W
Motor: V=12V, I=2A
R = 12/2 = 6 Ω
P = 12 × 2 = 24 WSeries vs Parallel Resistance
Series: R_total = R1 + R2 + R3
Parallel: 1/R_total = 1/R1 + 1/R2 + 1/R3
Two equal parallel: R_total = R/2Safety Note
- Household circuits: 120V or 240V — always fatal potential
- Safe low-voltage: < 50V DC for most applications
- Always calculate current draw before wiring
- Fuse rating = 125% of expected maximum current
Calculate circuit values: Free Ohm's Law Calculator
The Four Forms of Ohm's Law
- Voltage: V = IR (volts)
- Current: I = V/R (amperes)
- Resistance: R = V/I (ohms, Ω)
- Power: P = VI = I²R = V²/R (watts)
Practical Circuit Analysis
Ohm's Law is the foundation of all circuit analysis. In series circuits, total resistance R_total = R₁ + R₂ + R₃; current is the same throughout; voltage divides across resistors proportionally. In parallel circuits, 1/R_total = 1/R₁ + 1/R₂ + 1/R₃; voltage is the same across all; current divides inversely proportional to resistance. Real applications: sizing fuses and breakers (maximum current = V/R_load), calculating power dissipation in resistors (ensure P_actual < P_rated), designing voltage dividers, and troubleshooting circuits by measuring voltage drops.
Frequently Asked Questions
Does Ohm's Law apply to all components?
Ohm's Law applies only to ohmic (linear) resistors where V/I is constant regardless of voltage or current. Many components are non-ohmic: diodes (non-linear V-I characteristic), transistors, LEDs (conduct only above a threshold voltage), and capacitors/inductors (impedance depends on frequency). For AC circuits with reactive components, Ohm's Law generalises to V = IZ where Z is complex impedance.
What happens when resistance is zero?
In a superconductor, resistance = 0 and current flows without voltage and without power loss. In a practical short circuit, resistance approaches zero, current becomes very large (limited only by wiring resistance and source impedance), and power dissipation (I²R) can cause fire or equipment damage. This is why fuses and circuit breakers are essential — they interrupt the circuit before dangerous currents flow.
What is the difference between resistance and impedance?
Resistance (R) is the opposition to DC current flow, frequency-independent. Impedance (Z) is the complex generalisation for AC circuits, including resistive (R), inductive (jωL), and capacitive (1/jωC) components. |Z| = √(R² + X²) where X is reactance. At DC (f=0), capacitors are open circuits and inductors are short circuits.