Ohm's Law formula example
What is the Ohm's Law formula?
V = I × R (Voltage equals Current times Resistance)
| Find | Formula | Example |
|---|---|---|
| Voltage (V) | V = I × R | 2A × 10Ω = 20V |
| Current (I) | I = V / R | 20V ÷ 10Ω = 2A |
| Resistance (R) | R = V / I | 20V ÷ 2A = 10Ω |
For all Ohms Law formulas, the full 12-formula wheel below covers voltage, current, resistance, and power.
→ Use the Ohm's Law Calculator for instant calculations.
For a printable formula reference, open the Ohm's Law Formula Chart. If the problem expands beyond one load, continue to the Series Circuit Calculator or Parallel Circuit Calculator before moving into voltage drop or power sizing.
The Three Ohm's Law Formulas
Core Relationship
Ohm's Law describes the relationship between voltage, current, and resistance in an electrical circuit:
V = I × R
This single equation gives us three formulas:
| To Find | Formula | Unit | Symbol |
|---|---|---|---|
| Voltage | V = I × R | Volts | V |
| Current | I = V / R | Amperes | A |
| Resistance | R = V / I | Ohms | Ω |
Understanding the Variables
| Variable | Name | Unit | Description |
|---|---|---|---|
| V | Voltage | Volts (V) | Electrical pressure or potential difference |
| I | Current | Amperes (A) | Flow of electrons through a conductor |
| R | Resistance | Ohms (Ω) | Opposition to current flow |
Ohm's Law Wheel (Formula Reference)
Complete Ohm's Law Wheel
The Ohm's Law wheel shows all 12 formulas for calculating voltage, current, resistance, and power:
Voltage (V) Formulas:
V = I × R
V = P / I
V = √(P × R)
Current (I) Formulas:
I = V / R
I = P / V
I = √(P / R)
Resistance (R) Formulas:
R = V / I
R = P / I²
R = V² / P
Power (P) Formulas:
P = V × I
P = I² × R
P = V² / R
Quick Reference Table
| Known Values | Find V | Find I | Find R | Find P |
|---|---|---|---|---|
| I and R | V = I×R | — | — | P = I²×R |
| V and R | — | I = V/R | — | P = V²/R |
| V and I | — | — | R = V/I | P = V×I |
| P and I | V = P/I | — | R = P/I² | — |
| P and R | V = √(P×R) | I = √(P/R) | — | — |
| P and V | — | I = P/V | R = V²/P | — |
Power Formulas (Extended Ohm's Law)
Three Power Equations
Combine Ohm's Law with the power formula P = V × I:
| Formula | When to Use | Example |
|---|---|---|
| P = V × I | Know voltage and current | 120V × 10A = 1200W |
| P = I² × R | Know current and resistance | (10A)² × 12Ω = 1200W |
| P = V² / R | Know voltage and resistance | (120V)² ÷ 12Ω = 1200W |
Power Triangle
P
/ \
/ \
V × I
Cover what you want to find:
- Cover P → Multiply V × I
- Cover V → Divide P ÷ I
- Cover I → Divide P ÷ V
DC Circuit Calculations
Single Resistor Circuit
Given: 12V battery, 4Ω resistor
| Find | Calculation | Result |
|---|---|---|
| Current | I = V/R = 12V ÷ 4Ω | 3A |
| Power | P = V×I = 12V × 3A | 36W |
Series Resistor Circuit
For resistors in series: R_total = R₁ + R₂ + R₃ + ...
Given: 24V source, R₁ = 4Ω, R₂ = 8Ω
| Step | Calculation | Result |
|---|---|---|
| Total resistance | R = 4Ω + 8Ω | 12Ω |
| Current | I = 24V ÷ 12Ω | 2A |
| V across R₁ | V₁ = 2A × 4Ω | 8V |
| V across R₂ | V₂ = 2A × 8Ω | 16V |
Parallel Resistor Circuit
For resistors in parallel: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...
Given: 12V source, R₁ = 4Ω, R₂ = 6Ω
| Step | Calculation | Result |
|---|---|---|
| Total resistance | 1/R = 1/4 + 1/6 = 5/12 → R = 2.4Ω | 2.4Ω |
| Total current | I = 12V ÷ 2.4Ω | 5A |
| I through R₁ | I₁ = 12V ÷ 4Ω | 3A |
| I through R₂ | I₂ = 12V ÷ 6Ω | 2A |
→ Use Parallel Resistor Calculator for complex combinations.
AC Circuit Applications
Ohm's Law with Impedance
For AC circuits, resistance (R) becomes impedance (Z):
V = I × Z
Where impedance includes resistance and reactance:
Z = √(R² + X²)
| Component | Reactance Formula | Notes |
|---|---|---|
| Resistor | X_R = 0 | Pure resistance |
| Inductor | X_L = 2πfL | Increases with frequency (f = 60Hz in US) |
| Capacitor | X_C = 1/(2πfC) | Decreases with frequency (f = 60Hz in US) |
AC Circuit Example
Given: 120V AC, R = 6Ω, X_L = 8Ω (inductive load at 60Hz)
| Step | Calculation | Result |
|---|---|---|
| Impedance | Z = √(6² + 8²) = √100 | 10Ω |
| Current | I = 120V ÷ 10Ω | 12A |
| Power factor | PF = R/Z = 6/10 | 0.6 (lagging) |
| Real power | P = V×I×PF = 120×12×0.6 | 864W |
→ Learn more: Impedance and Reactance Guide
Worked Examples
Example 1: Find Voltage
Given: A circuit has 5A of current flowing through a 24Ω resistor.
Find: Voltage across the resistor
Solution:
V = I × R
V = 5A × 24Ω
V = 120V
Answer: The voltage is 120V.
Example 2: Find Current
Given: A 240V US circuit with a 60Ω heating element.
Find: Current flowing through the element
Solution:
I = V / R
I = 240V ÷ 60Ω
I = 4A
Answer: The current is 4A.
Example 3: Find Resistance
Given: A 12V LED strip drawing 0.5A.
Find: Resistance of the strip
Solution:
R = V / I
R = 12V ÷ 0.5A
R = 24Ω
Answer: The resistance is 24Ω.
Example 4: Find Power (All Methods)
Given: 120V circuit with 10Ω load
Method 1 (using V and R):
I = V/R = 120V ÷ 10Ω = 12A
P = V × I = 120V × 12A = 1440W
Method 2 (direct):
P = V²/R = (120V)² ÷ 10Ω = 14400 ÷ 10 = 1440W
Answer: Power consumption is 1440W.
Example 5: Wire Resistance Calculation
Given: 100 feet of 12 AWG copper wire (US typical resistance: 1.588Ω per 1000 ft)
Find: Voltage drop with 15A current
Solution:
Wire resistance = 1.588Ω × (100/1000) × 2 = 0.318Ω (round trip)
V_drop = I × R = 15A × 0.318Ω = 4.77V
Answer: Voltage drop is approximately 4.8V (4.0% of 120V - within an acceptable range for branch circuits depending on feeder drop, though the US NEC ideally recommends less than 3% drop for branch circuits alone for optimal efficiency).
Common Values Reference
Standard Resistor Values
E12 series (10% tolerance):
| Decade | Values |
|---|---|
| 1-10 | 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2 |
| 10-100 | 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 |
| 100-1k | 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 |
| 1k-10k | 1k, 1.2k, 1.5k, 1.8k, 2.2k, 2.7k, 3.3k, 3.9k, 4.7k, 5.6k, 6.8k, 8.2k |
Typical US Load Resistances
| Load Type | Typical Resistance | At Voltage | Power |
|---|---|---|---|
| 100W incandescent | 144Ω | 120VAC | 100W |
| 60W incandescent | 240Ω | 120VAC | 60W |
| 1500W space heater | 9.6Ω | 120VAC | 1500W |
| 12V 55W halogen | 2.6Ω | 12VDC | 55W |
| 5V USB charging | 2.5Ω | 5VDC | 10W |
Unit Conversions
Metric Prefixes for Electrical Units
| Prefix | Symbol | Multiplier | Example |
|---|---|---|---|
| Mega (M) | MΩ | × 1,000,000 | 2.2MΩ = 2,200,000Ω |
| Kilo (k) | kΩ | × 1,000 | 4.7kΩ = 4,700Ω |
| Base | Ω | × 1 | 100Ω |
| Milli (m) | mA | × 0.001 | 500mA = 0.5A |
| Micro (μ) | μA | × 0.000001 | 100μA = 0.0001A |
Quick Conversion Table
| mA to A | kΩ to Ω | mV to V |
|---|---|---|
| 1 mA = 0.001 A | 1 kΩ = 1000 Ω | 1 mV = 0.001 V |
| 100 mA = 0.1 A | 2.2 kΩ = 2200 Ω | 100 mV = 0.1 V |
| 500 mA = 0.5 A | 4.7 kΩ = 4700 Ω | 500 mV = 0.5 V |
| 1000 mA = 1 A | 10 kΩ = 10000 Ω | 1000 mV = 1 V |
Common Mistakes to Avoid
| Mistake | Why It's Wrong | Correct Approach |
|---|---|---|
| Mixing units (kΩ with A) | Wrong result | Convert to the same unit system (base units) first |
| Forgetting wire resistance | Underestimated voltage drop | Include round-trip wire resistance for single-phase |
| Using R for AC impedance | Ignores reactance | Use Z = √(R² + X²) for AC circuits with motors/coils |
| Confusing series/parallel | Wrong total resistance | Series: add directly; Parallel: reciprocal sum |
Related Calculators
| Calculator | Use When... |
|---|---|
| Ohm's Law Calculator | Quick V, I, R, P calculations |
| Parallel Resistor Calculator | Finding combined resistance |
| Series Circuit Calculator | Single-path circuit voltage/current checks |
| Parallel Circuit Calculator | Branch current and equivalent resistance checks |
| Voltage Drop Calculator | Wire sizing and measuring voltage loss |
| Power Calculator | General electrical power calculations |
| Ohm's Law Formula Chart | Printable V, I, R, P formula reference |
Summary
Core Formulas:
- V = I × R (Voltage = Current × Resistance)
- I = V / R (Current = Voltage ÷ Resistance)
- R = V / I (Resistance = Voltage ÷ Current)
Power Formulas:
- P = V × I
- P = I² × R
- P = V² / R
Memory Tip: Use the triangle method - cover what you want to find:
- Cover V → I × R (multiply)
- Cover I → V / R (divide)
- Cover R → V / I (divide)
FAQ
What is Ohm's Law in simple terms?
Ohm's Law states that current through a conductor is directly proportional to voltage and inversely proportional to resistance. More voltage = more current; more resistance = less current.
What are the units for Ohm's Law?
- Voltage: Volts (V)
- Current: Amperes or Amps (A)
- Resistance: Ohms (Ω)
- Power: Watts (W)
Does Ohm's Law apply to AC circuits?
Yes, but you must use impedance (Z) instead of simple resistance (R) if inductive or capacitive loads exist. Impedance accounts for both pure resistance and reactance from inductors and capacitors.
How do I calculate power using Ohm's Law?
Use any of these equivalent formulas: P = V × I, P = I² × R, or P = V² / R. Choose based on which values you know.
Why is it called "Ohm's" Law?
It is named after German physicist Georg Simon Ohm who first described this relationship in 1827. The unit of measurement for resistance (Ohm, Ω) is also named in his honor.