Ohm's Law Calculator
Calculate voltage, current, resistance, and power instantly using Ohm's Law (V=IR) and the power equation (P=VI). Enter any two known electrical values to solve for the remaining two with step-by-step solutions and unit conversions.
Enter any two values to calculate the remaining two.
This calculator assumes ideal ohmic DC circuit conditions. For AC circuits, impedance (Z) should be used instead of resistance (R).
What Is Ohm's Law and How Does It Work?
Ohm's Law is one of the most fundamental principles in electrical engineering and physics. Discovered by German physicist Georg Simon Ohm in 1827, this law defines the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. The law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. This simple yet powerful relationship is expressed mathematically as V = IR, where V is voltage in volts, I is current in amperes, and R is resistance in ohms.
Georg Ohm published his findings in his 1827 work 'Die galvanische Kette, mathematisch bearbeitet' (The Galvanic Circuit Investigated Mathematically). His discovery was initially met with skepticism from the scientific community, but it eventually became one of the cornerstones of electrical science. Ohm's Law provides the foundation for analyzing and designing every electrical circuit, from the simplest flashlight to the most complex computer processor. The unit of electrical resistance, the ohm (Ω), was named in his honor in 1881 by the International Electrical Congress.
In practical terms, Ohm's Law tells us three essential things: if you increase the voltage across a circuit while keeping resistance constant, the current increases proportionally; if you increase the resistance while keeping voltage constant, the current decreases; and if you know any two of the three values (voltage, current, resistance), you can always calculate the third. This makes Ohm's Law an indispensable tool for electricians, engineers, hobbyists, and students working with any kind of electrical system.
Beyond the basic V=IR relationship, Ohm's Law extends naturally to electrical power calculations. Power (P), measured in watts, can be calculated using three equivalent formulas derived from Ohm's Law: P = VI (power equals voltage times current), P = I²R (power equals current squared times resistance), and P = V²/R (power equals voltage squared divided by resistance). Together, these relationships form the complete Ohm's Law power wheel, which our calculator uses to solve for any unknown values from just two known inputs.
How to Calculate Voltage, Current, Resistance, and Power
Ohm's Law and the power equation give you 12 formulas to find any electrical value from two known values. Here are the core formulas organized by what you want to calculate:
Voltage equals current multiplied by resistance. If 2 amps flow through a 6-ohm resistor, the voltage across it is V = 2 × 6 = 12 volts. You can also find voltage from power: V = P / I or V = √(P × R).
Current equals voltage divided by resistance. A 12V battery connected to a 4-ohm resistor produces I = 12 / 4 = 3 amps of current. Alternative formulas: I = P / V or I = √(P / R).
Resistance equals voltage divided by current. If 9 volts drives 0.5 amps through a component, its resistance is R = 9 / 0.5 = 18 ohms. You can also calculate R = V² / P or R = P / I².
Power equals voltage multiplied by current. A 120V outlet supplying 0.5 amps delivers P = 120 × 0.5 = 60 watts. Alternative formulas: P = I² × R or P = V² / R.
Remember the Ohm's Law wheel: place the unknown value at the center and use any two known values from the surrounding formulas. With just two electrical quantities, you can always calculate the other two.
Electrical Quantities at a Glance
The four fundamental electrical quantities in Ohm's Law are interconnected. Understanding each quantity and its unit is essential for circuit analysis and design.
| Quantity | Symbol | Unit |
|---|---|---|
| Voltage | V | Volt (V) |
| Current | I | Ampere (A) |
| Resistance | R | Ohm (Ω) |
| Power | P | Watt (W) |
Limitations of Ohm's Law Calculations
While Ohm's Law is fundamental to electrical circuit analysis, it has inherent limitations that users should be aware of when applying it to real-world situations:
Linear (Ohmic) Components Only
Ohm's Law strictly applies only to ohmic materials and components — those where the voltage-current relationship is linear and passes through the origin. Many common electronic components are non-ohmic: diodes conduct current in only one direction and have an exponential V-I curve; LEDs have a threshold forward voltage before they conduct; transistors have complex V-I characteristics that depend on their operating region. For these components, Ohm's Law can only be applied over small, approximately linear regions of their characteristic curves.
No Temperature Effects on Resistance
This calculator assumes resistance remains constant regardless of temperature. In reality, the resistance of most conductors increases with temperature — a tungsten light bulb filament has about 10 times higher resistance when hot (operating) compared to cold (off). Semiconductors exhibit the opposite behavior, decreasing in resistance as temperature rises. For precise calculations in environments with significant temperature variation, you must account for the temperature coefficient of resistance (α): R(T) = R₀[1 + α(T – T₀)].
AC Circuits Require Impedance, Not Resistance
Ohm's Law in its basic form (V=IR) applies to DC circuits. In AC circuits, capacitors and inductors introduce reactance — opposition to current that varies with frequency. The combined effect of resistance and reactance is called impedance (Z), and the AC version of Ohm's Law becomes V = IZ, where Z is a complex number. At 60 Hz household frequency, a circuit with a 100Ω resistor and a 26.5 mF capacitor has an impedance of approximately 141Ω at 45° phase angle, not simply 100Ω.
Assumes Ideal Conditions
Ohm's Law calculations assume ideal conditions: perfect conductors with zero wire resistance, no contact resistance at connections, steady-state operation with no transient effects, and no electromagnetic interference. In practice, every connection adds some resistance (typically milliohms), long wire runs create voltage drops, and switching circuits experience transient spikes. Professional electrical designs always include safety margins — typically 20–25% derating — to account for these non-ideal factors.
Cannot Handle Complex Circuit Topologies
While Ohm's Law applies to individual components, analyzing complex circuits with multiple components in series, parallel, and series-parallel combinations requires additional tools: Kirchhoff's Voltage Law (KVL), Kirchhoff's Current Law (KCL), mesh analysis, or nodal analysis. Our calculator solves for a single component or a simple circuit where two values are known. For multi-component circuit analysis, consider using circuit simulation software such as SPICE, LTspice, or Falstad's circuit simulator.
No Frequency-Dependent Effects
At high frequencies (typically above 1 MHz), additional effects become significant that Ohm's Law does not account for. The skin effect causes current to concentrate near the surface of a conductor, effectively increasing its resistance. Parasitic capacitance between adjacent traces or wires can create unintended current paths. Parasitic inductance in leads and traces can cause significant voltage drops. At radio frequencies and above, transmission line theory and electromagnetic wave analysis replace simple Ohm's Law calculations.
Ohm's Law Across Different Circuit Types
Ohm's Law applies differently depending on the type of circuit you are working with. Understanding these variations is essential for correct application of the voltage-current-resistance-power relationships in different real-world scenarios.
DC (Direct Current) Circuits
DC circuits are where Ohm's Law applies most directly and accurately. In a DC circuit, voltage and current maintain constant values (in steady state), and resistance is purely resistive with no reactive components. Batteries, solar cells, USB power supplies, and DC adapters all provide direct current. The formulas V=IR, I=V/R, R=V/I, P=VI, P=I²R, and P=V²/R all apply without modification in DC circuits.
Common DC circuit analysis includes calculating the current drawn by a device from a battery, determining the voltage drop across a resistor in a voltage divider, finding the power dissipated by a heating element, and sizing fuses or circuit protection. For series DC circuits, the total resistance is the sum of individual resistances (R_total = R1 + R2 + R3), and the same current flows through all components. The voltage divides proportionally across each resistor according to its resistance value.
AC (Alternating Current) Circuits
In AC circuits, Ohm's Law is generalized to V = IZ, where Z is impedance — a complex quantity that includes both resistance (R) and reactance (X). Reactance comes from capacitors (X_C = 1/(2πfC)) and inductors (X_L = 2πfL), and it depends on the frequency of the AC signal. Impedance magnitude is calculated as |Z| = √(R² + X²), and the phase angle between voltage and current is θ = arctan(X/R).
For purely resistive AC loads (such as incandescent bulbs and electric heaters), Ohm's Law works the same as in DC circuits using RMS (root-mean-square) values of voltage and current. For loads with reactive components (motors, fluorescent ballasts, power supplies), you must distinguish between apparent power (S = VI, in volt-amperes), real power (P = VI·cosθ, in watts), and reactive power (Q = VI·sinθ, in vars). The power factor (cosθ) indicates how efficiently the load converts electrical power into useful work.
Series Circuits
In a series circuit, components are connected end-to-end in a single path. The same current (I) flows through every component. The total resistance is the sum of all individual resistances: R_total = R1 + R2 + R3 + ... The total voltage equals the sum of voltage drops across each component: V_total = V1 + V2 + V3 + ... Using Ohm's Law, the voltage drop across any single resistor is V_n = I × R_n.
Series circuits are used in voltage dividers, string lights (older Christmas lights), current-limiting resistors for LEDs, and many sensor circuits. A key property of series circuits is that if any component fails open (breaks), the entire circuit stops working because the current path is interrupted. The total power in a series circuit is the sum of power dissipated by each component: P_total = P1 + P2 + P3 = I²(R1 + R2 + R3).
Parallel Circuits
In a parallel circuit, components are connected across the same two nodes, so each component has the same voltage (V) across it. The total current divides among the parallel branches: I_total = I1 + I2 + I3 + ... The total resistance is found using the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... For two resistors in parallel, the shortcut formula is R_total = (R1 × R2) / (R1 + R2).
Parallel circuits are the standard configuration for household wiring — all outlets in a room share the same 120V (or 230V) supply, and each appliance draws current independently. If one device is turned off or unplugged, the others continue to operate normally. The total resistance of a parallel combination is always less than the smallest individual resistance. Using Ohm's Law, the current through any branch is I_n = V / R_n, and the total power is P_total = V²/R1 + V²/R2 + V²/R3.
Why Understanding Ohm's Law Matters
Ohm's Law is the gateway to understanding all of electrical engineering and electronics. Every circuit you encounter — from a simple LED circuit to a complex microprocessor — can be analyzed using Ohm's Law as a starting point. Electricians use it daily to determine correct wire gauges, fuse ratings, and circuit breaker sizes to ensure safe installations. Using a wire that is too thin for the current it carries can cause overheating and potentially start a fire.
For electronics hobbyists and makers, Ohm's Law is essential for designing circuits with Arduino, Raspberry Pi, and other microcontrollers. Calculating the correct resistor value for an LED is one of the most common applications: if you have a 5V supply and an LED that needs 20mA at a 2V forward voltage, Ohm's Law tells you that you need R = (5-2) / 0.020 = 150 ohms. Without this calculation, you risk burning out your LED or not providing enough current for it to light up properly.
In professional electrical engineering, Ohm's Law forms the basis for power distribution planning, transmission line design, and energy efficiency analysis. Power companies must calculate voltage drops over long transmission lines to ensure adequate voltage reaches consumers. Industrial engineers use power calculations (P = I²R) to estimate heat generation in components and design appropriate cooling systems. Understanding the relationship between voltage, current, resistance, and power is fundamental to designing reliable, efficient, and safe electrical systems.
From an educational perspective, Ohm's Law is typically the first quantitative relationship students learn in physics and electrical engineering courses. Mastering this law provides the foundation for more advanced topics including Kirchhoff's laws, Thevenin's theorem, AC circuit analysis, and semiconductor physics. Our Ohm's Law calculator helps students verify their manual calculations, explore relationships between electrical quantities, and build intuition about how changes in one quantity affect the others.
Who Should Use an Ohm's Law Calculator
Students studying physics, electrical engineering, or electronics benefit enormously from an Ohm's Law calculator. Whether you are solving homework problems, preparing for exams, or working on lab assignments, this calculator helps you verify your work and understand the relationships between voltage, current, resistance, and power. The step-by-step solutions show exactly which formula is used and how the calculation proceeds, reinforcing your learning.
Electricians and electrical contractors use Ohm's Law calculations routinely when planning installations, sizing conductors, selecting protective devices, and troubleshooting circuits. Quickly calculating the current draw of a 1,500W space heater on a 120V circuit (I = 1500/120 = 12.5A) helps determine whether the existing circuit can handle the load safely without tripping the breaker.
Electronics hobbyists, makers, and DIY enthusiasts who work with Arduino, Raspberry Pi, LED projects, and custom circuits need Ohm's Law for component selection. Choosing the right resistor, ensuring your power supply can deliver enough current, and verifying that components won't exceed their power ratings are all tasks that rely on these fundamental calculations.
Audio engineers, automotive electricians, solar panel installers, and telecommunications technicians all regularly apply Ohm's Law in their specialized fields. Whether you are designing a speaker crossover network, diagnosing a car's electrical fault, sizing inverter cables for a solar system, or calculating signal loss in a cable run, Ohm's Law provides the essential framework for analysis and design.
Ohm's Law Calculation Methods Compared
Several tools and methods exist for calculating electrical quantities. Here is how our Ohm's Law calculator compares to other common approaches for determining voltage, current, resistance, and power.
| Method | How It Works | Advantages | Limitations |
|---|---|---|---|
| Ohm's Law Formulas (This Calculator) | V=IR, P=VI and derived formulas from two known values | Instant results; all 12 formula variations; step-by-step solutions; supports unit prefixes; works offline; educational | Assumes ideal/ohmic conditions; DC only; single component at a time |
| Digital Multimeter (DMM) | Directly measures voltage, current, or resistance using electronic sensors | Measures actual circuit values; works on live circuits; detects real-world non-idealities; portable | Requires physical access to circuit; measures one quantity at a time; accuracy varies with quality; cannot measure power directly |
| Circuit Simulator (SPICE/LTspice) | Numerical simulation of complete circuit behavior using component models | Handles complex circuits; models non-linear components; simulates AC and transient behavior; visualizes waveforms | Steep learning curve; requires accurate component models; computationally intensive for large circuits; no physical validation |
| Oscilloscope | Displays voltage waveforms over time on a screen for visual analysis | Shows time-varying signals; reveals transients and noise; high bandwidth; triggers on events | Expensive; measures voltage only (current via shunt resistor); requires probing skills; does not directly calculate power or resistance |
| Clamp Meter | Measures current by detecting the magnetic field around a conductor without breaking the circuit | Non-invasive current measurement; safe for high-current circuits; quick readings; combines multimeter functions | Less accurate than direct measurement; minimum current threshold; affected by nearby conductors; AC clamps cannot measure DC (hall-effect models can) |
Ohm's Law Formulas (This Calculator)
- How It Works
- V=IR, P=VI and derived formulas from two known values
- Advantages
- Instant results; all 12 formula variations; step-by-step solutions; supports unit prefixes; works offline; educational
- Limitations
- Assumes ideal/ohmic conditions; DC only; single component at a time
Digital Multimeter (DMM)
- How It Works
- Directly measures voltage, current, or resistance using electronic sensors
- Advantages
- Measures actual circuit values; works on live circuits; detects real-world non-idealities; portable
- Limitations
- Requires physical access to circuit; measures one quantity at a time; accuracy varies with quality; cannot measure power directly
Circuit Simulator (SPICE/LTspice)
- How It Works
- Numerical simulation of complete circuit behavior using component models
- Advantages
- Handles complex circuits; models non-linear components; simulates AC and transient behavior; visualizes waveforms
- Limitations
- Steep learning curve; requires accurate component models; computationally intensive for large circuits; no physical validation
Oscilloscope
- How It Works
- Displays voltage waveforms over time on a screen for visual analysis
- Advantages
- Shows time-varying signals; reveals transients and noise; high bandwidth; triggers on events
- Limitations
- Expensive; measures voltage only (current via shunt resistor); requires probing skills; does not directly calculate power or resistance
Clamp Meter
- How It Works
- Measures current by detecting the magnetic field around a conductor without breaking the circuit
- Advantages
- Non-invasive current measurement; safe for high-current circuits; quick readings; combines multimeter functions
- Limitations
- Less accurate than direct measurement; minimum current threshold; affected by nearby conductors; AC clamps cannot measure DC (hall-effect models can)
Practical Guide to Using Ohm's Law
Whether you are wiring a home, building an electronics project, or studying for an exam, here are practical tips and real-world examples for applying Ohm's Law effectively.
Choosing the Right Resistor for an LED
- 1.Identify the LED's forward voltage (V_f) and maximum forward current (I_f) from the datasheet. Common values: red LEDs have V_f ≈ 2.0V at 20mA, white/blue LEDs have V_f ≈ 3.0–3.3V at 20mA.
- 2.Calculate the required resistor value: R = (V_supply – V_f) / I_f. For a red LED on a 5V Arduino pin: R = (5 – 2.0) / 0.020 = 150Ω. Choose the next standard resistor value up (150Ω or 180Ω for extra safety).
- 3.Check the resistor's power rating: P = I² × R = (0.020)² × 150 = 0.06W. A standard 1/4W (0.25W) resistor is more than adequate. Always verify that the resistor can handle the calculated power.
- 4.For multiple LEDs in series, add up the forward voltages and use the same formula. For three red LEDs on 12V: R = (12 – 6.0) / 0.020 = 300Ω. Parallel LEDs each need their own current-limiting resistor to ensure equal brightness.
Household Electrical Safety
- 1.Calculate appliance current draw before plugging into a circuit. A 1,800W hair dryer on 120V draws I = 1800/120 = 15A — this alone nearly maxes out a standard 15A household circuit. Running other appliances on the same circuit risks tripping the breaker.
- 2.Use Ohm's Law to check wire sizing. The National Electrical Code (NEC) specifies that 14-gauge wire handles up to 15A and 12-gauge wire handles up to 20A. Running 20A through 14-gauge wire exceeds its rating and creates a fire hazard due to excessive I²R heating.
- 3.Calculate voltage drop for long wire runs: V_drop = I × R_wire. For a 100-foot run of 14-gauge wire (2.525Ω per 1000 feet) carrying 15A: V_drop = 15 × (2 × 100 × 2.525/1000) = 7.6V — a 6.3% drop on 120V, which exceeds the recommended 3% maximum.
Electronics Design Tips
- 1.Use voltage dividers (two resistors in series) to reduce voltage levels. The output voltage is V_out = V_in × R2/(R1+R2). For a 5V to 3.3V divider, use R1 = 10kΩ and R2 = 20kΩ: V_out = 5 × 20k/(10k+20k) = 3.33V. Note: voltage dividers cannot supply significant current to a load.
- 2.Always calculate total power dissipation in your circuit and ensure your power supply can deliver it. Add up P = VI for each component. A circuit with five 330Ω resistors each carrying 20mA dissipates 5 × (0.020² × 330) = 0.66W total.
- 3.When measuring unknown resistance, use the voltmeter-ammeter method: apply a known voltage, measure the current, and calculate R = V/I. This is more accurate than a multimeter's resistance mode for very low or very high resistances.
Circuit Troubleshooting with Ohm's Law
- 1.If a circuit draws more current than expected, suspect a short circuit (near-zero resistance path) or a component failure. Use Ohm's Law to calculate what the current should be, then compare to the measured value.
- 2.If voltage is lower than expected at a point in the circuit, there may be excessive resistance upstream (a bad connection, corroded wire, or undersized conductor). Measure the voltage drop across suspected components and compare to Ohm's Law calculations.
- 3.For automotive electrical troubleshooting, a voltage drop of more than 0.1V across a connection or 0.2V across a switch usually indicates a problem. Use V = IR: if 10A flows through a connector and you measure 0.5V across it, the connector has R = 0.5/10 = 0.05Ω of resistance — likely due to corrosion or a loose connection.
Important Notes on Electrical Calculations
Ohm's Law calculations assume ideal conditions — linear (ohmic) components operating at constant temperature with pure DC (direct current). Real-world circuits often involve non-ideal conditions that can cause results to deviate from calculated values. Always include appropriate safety margins when designing circuits.
Ohm's Law calculations may be less accurate for:
- Non-ohmic devices such as diodes, transistors, and LEDs, where the relationship between voltage and current is nonlinear. These components have a voltage-current curve that does not follow a straight line through the origin.
- AC (alternating current) circuits where impedance replaces simple resistance. Impedance includes resistance plus reactance from capacitors and inductors, and varies with frequency. Use AC-specific formulas (V = IZ) for AC circuits.
- High-temperature environments where resistance changes significantly. Most conductors increase in resistance as temperature rises (positive temperature coefficient), while semiconductors typically decrease in resistance (negative temperature coefficient).
- High-frequency circuits where parasitic inductance, capacitance, and skin effect alter the effective resistance of conductors and components. At radio frequencies (RF), transmission line theory replaces simple Ohm's Law analysis.
For safety-critical applications such as household wiring, industrial power systems, or medical equipment, always consult a licensed electrician or engineer. This calculator is intended as an educational and quick-reference tool, not as a substitute for professional electrical design and code compliance.
Frequently Asked Questions About Ohm's Law
Ohm's Law states that the current (I) flowing through a conductor is directly proportional to the voltage (V) across it and inversely proportional to its resistance (R). The mathematical expression is V = IR, or equivalently I = V/R and R = V/I. Discovered by Georg Simon Ohm in 1827, this fundamental principle means that doubling the voltage across a fixed resistance doubles the current, while doubling the resistance at a fixed voltage halves the current. Ohm's Law applies to ohmic (linear) materials and is the foundation of virtually all electrical circuit analysis, from simple battery circuits to complex power distribution systems.
To calculate voltage using Ohm's Law, multiply the current (in amperes) by the resistance (in ohms): V = I × R. For example, if 3 amps of current flow through a 10-ohm resistor, the voltage across that resistor is V = 3 × 10 = 30 volts. Make sure your units are consistent — if current is in milliamps (mA), either convert to amps first (divide by 1000) or keep the result in millivolts (mV). You can also calculate voltage from power: V = P/I (voltage equals power divided by current) or V = √(P×R) (voltage equals the square root of power times resistance). All three formulas are derived from the same fundamental relationships.
To find current, divide the voltage by the resistance: I = V / R. This is the most commonly used rearrangement of Ohm's Law. For example, a 12-volt car battery connected to headlights with 2.4 ohms total resistance produces I = 12 / 2.4 = 5 amps of current. This formula is essential for determining whether a circuit will exceed the current rating of its wires, fuses, or circuit breakers. If you know power instead of resistance, use I = P / V (current equals power divided by voltage). A 60-watt light bulb on a 120-volt circuit draws I = 60/120 = 0.5 amps. Always verify that all components in the circuit path are rated for the calculated current.
Ohm's Law (V=IR) combines with the basic power equation (P=VI) to create a family of power formulas. By substituting Ohm's Law into P=VI, you get P = I²R (substituting V=IR) and P = V²/R (substituting I=V/R). These three power formulas are mathematically equivalent and let you calculate power from any two known electrical quantities. For example, if you know current (2A) and resistance (50Ω), power is P = 2² × 50 = 200W. If you know voltage (100V) and resistance (50Ω), power is P = 100²/50 = 200W. The P=I²R formula is particularly important for understanding heat generation in wires and components, since it shows that power (heat) increases with the square of the current.
Ohm's Law applies to AC circuits in a generalized form: V = IZ, where Z is impedance rather than simple resistance. Impedance is a complex quantity that includes both resistance (R) and reactance (X) from capacitors and inductors: Z = R + jX, where j is the imaginary unit. The magnitude of impedance is |Z| = √(R² + X²). For purely resistive AC loads (heaters, incandescent bulbs), Ohm's Law works identically to DC using RMS values. However, for circuits with capacitors or inductors, voltage and current are out of phase, and you must use impedance. Additionally, AC power analysis distinguishes between real power (watts), reactive power (vars), and apparent power (volt-amperes), connected by the power factor cosθ.
The most frequent mistakes include: (1) Unit inconsistency — mixing milliamps with amps or kilohms with ohms without converting. Always convert to base units (V, A, Ω, W) before calculating. (2) Applying Ohm's Law to non-ohmic devices like diodes, LEDs, or transistors, which do not have a linear V-I relationship. (3) Forgetting that Ohm's Law applies to individual components, not entire complex circuits without proper series/parallel simplification first. (4) Confusing voltage at a point with voltage across a component — voltage is always measured between two points. (5) Neglecting power ratings — calculating that a 100Ω resistor needs to carry 1A means it dissipates P = 1² × 100 = 100W, which would destroy a standard 1/4W resistor.
Ohm's Law is embedded in many daily decisions and technologies. When you check if your home circuit can handle a new appliance, you use P=VI: a 1,500W microwave on 120V draws 12.5A, which is significant for a 15A circuit. Phone chargers use Ohm's Law principles — fast chargers increase either voltage (USB-PD uses up to 20V) or current (Qualcomm Quick Charge) to deliver more power (P=VI) to charge batteries faster. Electricians use I=P/V to size circuit breakers and wire gauges for every room in your house. Automotive mechanics check battery health by measuring voltage under load. Even the dimmer switch on your wall works by varying the effective voltage to change current and thus power (brightness) delivered to the light.
Resistance (R, measured in ohms) is the opposition to current flow that converts electrical energy to heat. It is constant regardless of frequency and applies to DC and AC equally. Impedance (Z, also measured in ohms) is the total opposition to current in an AC circuit, combining resistance with reactance. Reactance comes from capacitors (capacitive reactance X_C = 1/(2πfC), which decreases with frequency) and inductors (inductive reactance X_L = 2πfL, which increases with frequency). Impedance is calculated as Z = √(R² + (X_L – X_C)²). In a pure DC circuit or a purely resistive AC circuit, impedance equals resistance. The distinction matters in audio systems, RF circuits, power distribution, and any application involving capacitors or inductors.
In series circuits, the same current flows through all components. Total resistance is the sum: R_total = R1 + R2 + R3. Apply Ohm's Law to find total current (I = V_total / R_total), then find the voltage drop across each resistor (V_n = I × R_n). In parallel circuits, the same voltage appears across all branches. Total resistance follows the reciprocal rule: 1/R_total = 1/R1 + 1/R2 + 1/R3. Apply Ohm's Law to find each branch current (I_n = V / R_n), then sum for total current. For example, two 100Ω resistors in series give 200Ω total; in parallel they give 50Ω total. For mixed series-parallel circuits, simplify parallel groups first, then add series resistances, working from the inside out.
Non-ohmic (or nonlinear) components have a voltage-current relationship that is not a straight line. Common examples include: (1) Diodes and LEDs, which conduct only in one direction and have an exponential V-I curve with a threshold voltage. (2) Transistors (BJTs, MOSFETs), whose current depends nonlinearly on a control voltage or current. (3) Thermistors, whose resistance changes dramatically with temperature — NTC thermistors decrease in resistance when heated. (4) Varistors (MOVs), which have very high resistance below a threshold voltage but become highly conductive above it, used for surge protection. (5) Gas discharge tubes and fluorescent lamps, which exhibit negative resistance regions. (6) Superconductors, which have exactly zero resistance below their critical temperature. These components require their own characteristic equations rather than simple Ohm's Law.