Result
Voltage (V) = 12 V
Ohm's Law Triangle
V = I × R
Example Calculations
Example 1
I = 2 A, R = 5 Ω
V = I × R = 2 × 5
V = 10 V
Example 2
V = 9 V, R = 3 Ω
I = V / R = 9 / 3
I = 3 A
Example 3
V = 12 V, I = 2 A
R = V / I = 12 / 2
R = 6 Ω
Ohm's Law Educational Reference
Physical Significance and Theory
Ohm's Law, formulated by German physicist Georg Simon Ohm in 1827, describes the fundamental relationship between voltage (V), current (I), and resistance (R) in electrical circuits. The law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.
Mathematical Formulation
Derived Formulas
- Current: I = V ÷ R
- Resistance: R = V ÷ I
- Power (related): P = V × I = I² × R = V² ÷ R
Unit System and Conversions
This calculator uses the International System of Units (SI) as its base:
- Voltage: Volts (V) with milliVolts (mV = 10⁻³ V) option
- Current: Amperes (A) with milliamperes (mA = 10⁻³ A) option
- Resistance: Ohms (Ω) with kiloOhms (kΩ = 10³ Ω) option
All calculations are performed in base SI units and converted for display. For example, entering 500 mA automatically converts to 0.5 A for calculation.
Step-by-Step Calculation Process
- Variable Selection: Choose which quantity to calculate (V, I, or R)
- Input Normalization: All inputs are converted to base SI units:
- mV → V (divide by 1000)
- mA → A (divide by 1000)
- kΩ → Ω (multiply by 1000)
- Formula Application: The appropriate formula is applied based on selection
- Unit Optimization: Results are converted to the most readable unit:
- Voltage: V, mV, or kV
- Current: A or mA
- Resistance: Ω or kΩ
Accuracy Considerations
- Rounding: Results display with 2 decimal places for clarity
- Precision: Internal calculations use JavaScript's 64-bit floating point precision
- Unit Conversion: Exact conversion factors (1000, not 1024) are used
- Input Validation: Non-numeric inputs are treated as zero
Model Assumptions and Limitations
Important Notes
This calculator assumes ideal Ohmic conditions:
- Linear relationship: R is constant (independent of V and I)
- Constant temperature: Resistance doesn't change with heating
- DC conditions: For direct current applications
- Ohmic materials: Materials that obey Ohm's Law (metals at constant temperature)
Non-Ohmic Devices
Ohm's Law does not apply to:
- Semiconductors (diodes, transistors)
- Superconductors (R = 0 below critical temperature)
- Ionic solutions with electrolysis
- Devices with significant temperature dependence (incandescent bulbs)
- AC circuits with capacitance or inductance
Common Student Misconceptions
- Misconception: "Ohm's Law applies to all electrical devices"
Correction: Only applies to Ohmic conductors under constant conditions
- Misconception: "Resistance causes current"
Correction: Voltage causes current; resistance opposes it
- Misconception: "Higher resistance always means less current"
Correction: True only if voltage remains constant
- Misconception: "Current gets 'used up' in a circuit"
Correction: Current is conserved in series circuits
Real-World Applications
Engineering & Design
- Circuit design and component selection
- Power supply sizing and specification
- Voltage divider network design
- Current limiting resistor calculation for LEDs
- Fuse and circuit breaker selection
Education & Troubleshooting
- Laboratory experiments and measurements
- Circuit analysis and verification
- Fault diagnosis in electrical systems
- Multimeter measurement interpretation
- Electrical safety calculations
Frequently Asked Questions
Q: Can I use this calculator for AC circuits?
A: This calculator is designed for DC circuits. For AC circuits with reactive components (inductors, capacitors), you need to consider impedance (Z) instead of resistance (R) and phase angles.
Q: What happens if I enter zero resistance?
A: The calculator will show "N/A" for current calculation (division by zero). In real circuits, zero resistance represents a short circuit with theoretically infinite current (limited by power supply capacity).
Q: Why does my result show different units than I entered?
A: The calculator optimizes units for readability. For example, 0.005 A displays as 5 mA, and 1500 Ω displays as 1.5 kΩ.
Q: Is temperature considered in these calculations?
A: No, this calculator assumes constant temperature. In reality, resistance changes with temperature (positive coefficient for metals).
Related Physics Concepts
- Kirchhoff's Laws: For complex circuit analysis
- Power Calculations: P = V × I (Joule's Law)
- Series/Parallel Resistors: Different resistance combinations
- Electrical Conductivity: σ = 1/ρ (reciprocal of resistivity)
- Electromotive Force (EMF): Source voltage including internal resistance
Academic Integrity and References
This tool implements the standard Ohm's Law formulation as presented in:
- Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of Physics (10th ed.)
- Serway, R. A., & Jewett, J. W. (2018). Physics for Scientists and Engineers
- International System of Units (SI) - BIPM 9th edition
Educational Use: This calculator is intended for educational purposes and practical applications. For critical engineering designs, consult professional electrical engineering resources and consider all real-world factors.
Formula accuracy reviewed: April 15, 2025
Understanding Ohm's Law
Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. The law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them.
- Select the variable you want to calculate (V, I, or R)
- Enter the two known values in the input fields
- Select appropriate units for each value
- The calculator will automatically display the result
- Use the graph to visualize the relationship between voltage and current
- Circuit Design: Determine appropriate resistor values for desired current
- Troubleshooting: Identify issues in circuits by measuring voltage and current
- Power Supplies: Calculate current draw for proper power supply selection
- LED Circuits: Calculate required resistors for LEDs based on supply voltage