The Quick Answer
Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, expressed as V = I * R, where V is voltage in volts, I is current in amperes, and R is resistance in ohms.
If you know any two of the three quantities, you can calculate the third:
- V = I * R (find voltage)
- I = V / R (find current)
- R = V / I (find resistance)
That single relationship is the foundation of virtually all circuit analysis. The rest of this article covers how to apply it, including power formulas, worked circuit examples, and the cases where it breaks down.
The Three Forms of Ohm's Law
Georg Simon Ohm published his law in 1827 after measuring how current changes with voltage across different conductors. The relationship is linear for most common conductors and resistors (NIST reference on electrical units).
Form 1: V = I * R
Use this when you know current and resistance and need to find voltage. A current of 2A flowing through a 10-ohm resistor produces a voltage drop of 2 * 10 = 20V across that resistor.
Form 2: I = V / R
Use this when you know voltage and resistance and need to find current. A 12V battery connected across a 4-ohm load drives a current of 12 / 4 = 3A.
Form 3: R = V / I
Use this when you know voltage and current and need to find resistance. If 120V drives 10A through a heating element, the element's resistance is 120 / 10 = 12 ohms.
The Ohm's Law Wheel
A common reference diagram places V at the top and I and R side by side at the bottom, forming a triangle. Cover the quantity you want to find: if you cover V, you see I * R; cover I, you see V / R; cover R, you see V / I. An expanded version adds power (P) in a second ring, giving twelve formula variations that relate any two of the four quantities (V, I, R, P) to the other two.
Power Formulas
Electrical power -- measured in watts (W) -- tells you how quickly energy is consumed. Three equivalent formulas connect power to Ohm's Law:
- P = V * I (voltage times current)
- P = I^2 * R (current squared times resistance)
- P = V^2 / R (voltage squared divided by resistance)
These are not separate laws. Each one comes from substituting Ohm's Law into P = V * I. Use whichever form matches the values you already have.
Worked Example 1: LED Circuit Design
Problem: You have a 9V battery and an LED rated for 2V forward voltage at 20 mA. What resistor do you need?
Solution:
- The resistor must drop the difference between supply voltage and LED forward voltage: 9V - 2V = 7V
- The desired current is 20 mA = 0.020 A
- Apply R = V / I: R = 7 / 0.020 = 350 ohms
Standard resistor values do not include 350 ohms exactly. The nearest standard values in the E24 series are 330 and 360 ohms. Choosing 360 ohms (or 390 ohms for extra safety margin) slightly reduces the current:
- At 360 ohms: I = 7 / 360 = 19.4 mA
- At 390 ohms: I = 7 / 390 = 17.9 mA
Both are close to 20 mA and well within the LED's safe operating range. Power dissipated by the resistor: P = I^2 * R = (0.0194)^2 * 360 = 0.14W. A standard 1/4-watt (0.25W) resistor handles this easily.
Worked Example 2: Household Appliance
Problem: A 1,500W space heater plugs into a standard 120V outlet. What current does it draw, and what is the heater's resistance?
Solution:
- Find current: I = P / V = 1,500 / 120 = 12.5 A
- Find resistance: R = V / I = 120 / 12.5 = 9.6 ohms
This explains why space heaters require a dedicated 15A or 20A circuit. At 12.5A, the heater consumes most of a 15A circuit's capacity. Plugging a second high-draw device into the same circuit will likely trip the breaker.
Cross-check with power formula: P = V^2 / R = 120^2 / 9.6 = 14,400 / 9.6 = 1,500W. Confirmed.
Worked Example 3: Series vs. Parallel Resistors
Problem: You have two 100-ohm resistors. What is the total resistance in series and in parallel?
Series: Resistances add directly.
R_total = R1 + R2 = 100 + 100 = 200 ohms
If connected to a 10V source: I = 10 / 200 = 0.05A (50 mA). Each resistor drops 5V.
Parallel: Reciprocals add.
1/R_total = 1/100 + 1/100 = 2/100
R_total = 100/2 = 50 ohms
If connected to a 10V source: I = 10 / 50 = 0.2A (200 mA). Each resistor carries 100 mA.
The pattern holds generally: series always increases total resistance; parallel always decreases it below the smallest individual resistor.
Wire Gauge and Current Capacity
Ohm's Law applies to wires too. Every wire has resistance, and that resistance causes a voltage drop and generates heat. Thicker wire has lower resistance per unit length.
For example, 14 AWG copper wire (common for 15A household circuits) has a resistance of about 8.3 ohms per 1,000 feet. Carrying 15A through 100 feet (50 feet out and 50 feet back), the voltage drop is:
V_drop = I * R = 15 * (8.3 * 100/1000) = 15 * 0.83 = 12.5V
That is over 10% of 120V -- too much for most applications. This is why long runs need thicker wire. Upgrading to 12 AWG (5.2 ohms per 1,000 ft) drops the loss to about 7.8V, and 10 AWG (3.3 ohms per 1,000 ft) brings it down to about 5V. The National Electrical Code recommends no more than a 3% voltage drop for branch circuits.
Limitations of Ohm's Law
Ohm's Law assumes a linear, constant relationship between voltage and current. This holds for ohmic materials -- most metals, carbon resistors, and nichrome wire at constant temperature. It does not hold for:
- Diodes and LEDs: Current is nearly zero below a threshold voltage, then rises exponentially. The V-I curve is nonlinear.
- Transistors: Current depends on a control signal (base current or gate voltage), not just the voltage across the device.
- Thermistors: Resistance changes significantly with temperature.
- Superconductors: Resistance drops to exactly zero below a critical temperature.
- Gas discharge tubes: Resistance changes dramatically once the gas ionizes.
For these components, Ohm's Law still describes the instantaneous relationship (V = I * R at any specific operating point), but R is not constant -- it depends on voltage, current, temperature, or other factors.
In AC circuits, Ohm's Law extends to V = I * Z, where Z is impedance -- a complex quantity that includes resistance, capacitive reactance, and inductive reactance. The magnitude and phase of current depend on frequency, not just resistance (HyperPhysics, Georgia State University).
Practical Tips
Always check power ratings. Resistors are rated for maximum power dissipation (typically 1/8W, 1/4W, 1/2W, or 1W for through-hole types). Calculate P = I^2 * R and choose a resistor rated well above that value.
Use standard resistor values. Resistors come in standard series (E12, E24, E96). After calculating the ideal value, pick the nearest standard value. Rounding up slightly reduces current and is usually the safer choice.
Measure, do not assume. Component tolerances (typically 1%, 5%, or 10% for resistors) and real-world conditions mean actual values differ from calculated ones. A multimeter check takes seconds and catches errors before they cause damage.
Try It Yourself
Use the Ohm's Law calculator to quickly solve for voltage, current, resistance, or power. Enter any two known values and get the other two instantly. You can also use the voltage divider calculator for resistor network designs, or the power unit converter to convert between watts, horsepower, and other power units.
Frequently Asked Questions
What is Ohm's Law in simple terms?
Ohm's Law says that voltage equals current multiplied by resistance (V = I * R). If you know any two of the three quantities -- voltage, current, or resistance -- you can calculate the third. It is the most fundamental equation in circuit analysis.
How do I calculate resistance using Ohm's Law?
Rearrange the formula to R = V / I. Divide the voltage across the component (in volts) by the current flowing through it (in amperes) to get resistance in ohms. For example, 12V across a component with 3A flowing gives R = 12 / 3 = 4 ohms.
Does Ohm's Law work for AC circuits?
Ohm's Law applies to AC circuits when you replace simple resistance with impedance (Z), which accounts for resistance, capacitance, and inductance. The generalized form is V = I * Z. For purely resistive AC loads (like incandescent bulbs and heaters), V = I * R works directly.
What happens if resistance is zero?
If resistance is zero, theoretically infinite current would flow for any applied voltage -- this is a short circuit. In practice, wires and power sources have some internal resistance, but a near-zero-resistance path causes dangerously high current, overheating, and can start fires or damage equipment.
What is the difference between voltage and current?
Voltage (measured in volts) is the electrical pressure or potential difference that pushes charge through a circuit. Current (measured in amperes) is the rate at which charge actually flows. A common analogy: voltage is like water pressure, current is like the flow rate, and resistance is like the pipe diameter.
How do I calculate power from Ohm's Law?
Power (in watts) can be calculated three ways: P = V * I, P = I^2 * R, or P = V^2 / R. Use whichever form matches the two quantities you already know. For example, if you know current (2A) and resistance (10 ohms): P = 2^2 * 10 = 40W.
Why do I need a resistor with an LED?
LEDs have very low internal resistance once the forward voltage threshold is reached. Without a current-limiting resistor, too much current flows and the LED burns out instantly. The resistor value is R = (Supply voltage - LED forward voltage) / Desired current.
What are the units for Ohm's Law?
Voltage is measured in volts (V), current in amperes (A), and resistance in ohms (represented by the Greek letter omega). One ohm is defined as the resistance that allows one ampere of current to flow when one volt of potential difference is applied.
Does Ohm's Law apply to all materials?
No. Ohm's Law applies to ohmic (linear) materials like most metals and standard resistors, where resistance stays constant regardless of voltage. Non-ohmic components -- diodes, transistors, LEDs, and thermistors -- have a non-linear relationship between voltage and current.
How do resistors combine in series and parallel?
In series, resistances add directly: R_total = R1 + R2 + R3 + ... In parallel, reciprocals add: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... For two equal resistors of value R, series gives 2R and parallel gives R/2.