Ohm's Law Explained: Voltage, Current, and Resistance
Ohm's Law states that the current flowing through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. The formula is V = I x R, where V is voltage in volts, I is current in amperes, and R is resistance in ohms. Published by German physicist Georg Simon Ohm in 1827, this law is the foundation of virtually all electrical and electronic circuit analysis.
Quick Answer
- 1. V = I x R (Voltage = Current x Resistance).
- 2. Rearranged: I = V / R and R = V / I.
- 3. Power formulas: P = V x I = I² x R = V² / R.
- 4. Applies to ohmic (linear) materials where resistance stays constant. Does not apply to diodes, LEDs, or transistors.
Calculate voltage, current, or resistance
Enter any two values to solve for the third, plus power. Uses Ohm's Law and the power formula.
Use Ohm's Law Calculator FreeWhat Is Ohm's Law?
Ohm's Law describes the fundamental relationship between three electrical quantities: voltage (the driving force that pushes electrons through a circuit), current (the rate of electron flow), and resistance (the opposition to that flow).
Think of it like water flowing through a pipe. Voltage is the water pressure, current is the flow rate (gallons per minute), and resistance is the pipe diameter. Higher pressure (voltage) pushes more water (current) through the pipe. A narrower pipe (higher resistance) restricts the flow.
The Three Forms of Ohm's Law
The single equation V = I x R can be rearranged to solve for any of the three variables:
| Solve For | Formula | Units |
|---|---|---|
| Voltage (V) | V = I x R | Volts (V) |
| Current (I) | I = V / R | Amperes (A) |
| Resistance (R) | R = V / I | Ohms (omega) |
Worked Examples
Example 1: Finding Current
A 12V battery is connected to a 4-ohm resistor. How much current flows?
- I = V / R = 12 / 4 = 3 amps
Example 2: Finding Voltage
A circuit draws 0.5 amps through a 240-ohm resistor. What is the voltage?
- V = I x R = 0.5 x 240 = 120 volts
Example 3: Finding Resistance
A 9V battery powers an LED circuit drawing 20 milliamps (0.02 A). What total resistance is in the circuit?
- R = V / I = 9 / 0.02 = 450 ohms
The Ohm's Law Triangle (Power Wheel)
When you combine Ohm's Law (V = IR) with the power formula (P = VI), you get a set of 12 equations that can solve for any unknown given any two known values. The most commonly used are:
| To Find | Formula 1 | Formula 2 | Formula 3 |
|---|---|---|---|
| Power (P) | P = V x I | P = I² x R | P = V² / R |
| Voltage (V) | V = I x R | V = P / I | V = sqrt(P x R) |
| Current (I) | I = V / R | I = P / V | I = sqrt(P / R) |
| Resistance (R) | R = V / I | R = P / I² | R = V² / P |
Power Example
A 120V household circuit powering a toaster with 10 ohms of resistance:
- Current: I = 120 / 10 = 12 amps
- Power: P = 120 x 12 = 1,440 watts
- Verified: P = V² / R = 14,400 / 10 = 1,440 watts
Ohm's Law in Series Circuits
In a series circuit, components are connected end-to-end in a single path. The rules are:
- Current is the same through every component: I_total = I_1 = I_2 = I_3
- Voltage divides across components: V_total = V_1 + V_2 + V_3
- Resistances add: R_total = R_1 + R_2 + R_3
Series Example
Three resistors (100, 220, and 330 ohms) in series with a 9V battery:
- R_total = 100 + 220 + 330 = 650 ohms
- I = 9 / 650 = 0.01385 A (13.85 mA)
- V across 100 ohm = 0.01385 x 100 = 1.385V
- V across 220 ohm = 0.01385 x 220 = 3.046V
- V across 330 ohm = 0.01385 x 330 = 4.569V
- Total: 1.385 + 3.046 + 4.569 = 9.0V (confirmed)
Ohm's Law in Parallel Circuits
In a parallel circuit, components are connected across the same two points. The rules are:
- Voltage is the same across every branch: V_total = V_1 = V_2 = V_3
- Current divides among branches: I_total = I_1 + I_2 + I_3
- Reciprocal resistance: 1/R_total = 1/R_1 + 1/R_2 + 1/R_3
Parallel Example
Two resistors (200 and 300 ohms) in parallel with a 12V source:
- 1/R_total = 1/200 + 1/300 = 0.005 + 0.00333 = 0.00833
- R_total = 1 / 0.00833 = 120 ohms
- I_total = 12 / 120 = 0.1 A (100 mA)
- I through 200 ohm = 12/200 = 60 mA
- I through 300 ohm = 12/300 = 40 mA
- Total: 60 + 40 = 100 mA (confirmed)
Practical Applications of Ohm's Law
LED Resistor Calculation
To light an LED safely, you need a current-limiting resistor. If your power supply is 5V, the LED forward voltage is 2V, and the desired LED current is 20 mA:
- Voltage across resistor = 5 - 2 = 3V
- R = V / I = 3 / 0.02 = 150 ohms
Home Circuit Sizing
A 120V circuit with a 15-amp breaker can safely deliver: P = 120 x 15 = 1,800 watts. The NEC (National Electrical Code) recommends loading circuits to no more than 80% capacity, giving a practical limit of 1,440 watts. This is why a single kitchen circuit can run a toaster or microwave, but not both simultaneously.
Troubleshooting with Ohm's Law
Technicians use Ohm's Law to diagnose faults. If a 12V car headlight draws only 3 amps instead of the expected 5 amps, the resistance has increased from 2.4 ohms to 4 ohms. The extra resistance is likely from corrosion, a loose connection, or a damaged wire. This diagnostic approach, described by Fluke, is standard practice in automotive and industrial troubleshooting.
The Bottom Line
Ohm's Law (V = IR) is the most fundamental equation in electrical engineering. Combined with the power formula (P = VI), it lets you calculate any electrical quantity from two known values. Whether you are sizing a resistor for an LED, checking a home circuit's capacity, or diagnosing a wiring fault, Ohm's Law is the starting point.
Our free Ohm's Law calculator solves for voltage, current, resistance, and power. Enter any two values to get the other two instantly.
Frequently Asked Questions
What is the formula for Ohm's Law?
Ohm's Law is expressed as V = I x R, where V is voltage in volts, I is current in amperes (amps), and R is resistance in ohms. This formula can be rearranged to solve for any variable: I = V / R (to find current) and R = V / I (to find resistance). The law states that current through a conductor is directly proportional to voltage and inversely proportional to resistance. If you double the voltage across a fixed resistor, the current doubles. If you double the resistance at the same voltage, the current halves.
What are real-world applications of Ohm's Law?
Ohm's Law is used constantly in electronics, electrical engineering, and everyday troubleshooting. Electricians use it to size wires and circuit breakers for home wiring. Electronics hobbyists use it to calculate resistor values for LEDs. Automotive technicians use it to diagnose charging system problems. HVAC technicians use it to test motor windings. Even smartphone charger specifications (5V at 2A = 10W) are an application of Ohm's Law combined with the power formula. Technicians use unexpected current levels as diagnostic clues: lower-than-expected current often indicates increased resistance from corrosion or loose connections.
Does Ohm's Law apply to AC circuits?
Ohm's Law applies to AC (alternating current) circuits, but with modifications. In AC circuits, resistance is replaced by impedance (Z), which includes resistance plus the effects of capacitance and inductance. The AC version becomes V = I x Z. For purely resistive AC loads (like heaters and incandescent bulbs), standard Ohm's Law applies directly because impedance equals resistance. For circuits with capacitors or inductors (like motors and transformers), you must calculate impedance using Z = sqrt(R squared + (XL - XC) squared), where XL is inductive reactance and XC is capacitive reactance.
What is the relationship between Ohm's Law and electrical power?
Electrical power (P) in watts is calculated as P = V x I (voltage times current). By substituting Ohm's Law into the power formula, you get three useful equations: P = V x I, P = I squared x R, and P = V squared / R. These combined formulas are known as the Ohm's Law power wheel or Ohm's Law triangle. For example, a 120V circuit with a 60-ohm heating element: current I = 120/60 = 2 amps, and power P = 120 x 2 = 240 watts. These relationships are essential for sizing power supplies, calculating heat dissipation, and designing safe circuits.
When does Ohm's Law not apply?
Ohm's Law applies only to ohmic (linear) materials where resistance remains constant regardless of voltage. It does not apply to non-ohmic components like diodes, LEDs, transistors, and thermistors, whose resistance changes with voltage, current, or temperature. For example, an LED's resistance drops dramatically once the forward voltage threshold (typically 1.8 to 3.3V depending on color) is reached. Superconductors also violate Ohm's Law by having zero resistance below their critical temperature. In practical circuits with non-ohmic components, engineers use Ohm's Law for the resistive portions and device-specific models (like the Shockley diode equation) for the non-linear components.
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