Ohm’s Law
Part of Basic Electrical Circuits
The single most important relationship in electrical engineering: how voltage, current, and resistance are linked in every circuit.
Why This Matters
Ohm’s Law is the foundation of all electrical circuit design. It states a simple relationship that was not obvious before Georg Ohm published it in 1827: the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance. Everything else in electrical engineering builds from this.
In practical terms, Ohm’s Law answers the three most common questions that arise when designing or troubleshooting circuits:
- What current will this circuit draw? (I = V/R)
- What voltage drop will appear across this component? (V = IR)
- What resistance is needed to limit current to a safe value? (R = V/I)
A person who can apply Ohm’s Law fluently can design safe wiring, select correct wire gauges, size resistors for any purpose, calculate battery life, and diagnose circuit faults. Without it, electrical work is guesswork with predictable consequences: burned components, dead batteries, and fires.
The Law
V = I × R
Where:
- V = voltage (volts, V)
- I = current (amperes, A)
- R = resistance (ohms, Ω)
Rearranged:
- I = V / R
- R = V / I
The memory aid — Ohm’s Law triangle: Draw a triangle with V at the top and I, R side by side at the bottom. Cover the quantity you want to find:
- Cover V: the remaining I and R are side-by-side, meaning multiply → V = I × R
- Cover I: V is above R, meaning divide → I = V/R
- Cover R: V is above I, meaning divide → R = V/I
Understanding the Relationship
Current proportional to voltage: Double the voltage across a fixed resistance and the current doubles. This makes intuitive sense—greater electrical “pressure” drives more flow.
Current inversely proportional to resistance: Double the resistance at a fixed voltage and the current halves. More opposition to flow means less flow—as with a narrower pipe restricting water flow.
Ohmic vs. non-ohmic materials: Materials that obey Ohm’s Law (resistance stays constant regardless of voltage or current) are called ohmic conductors. Metals at constant temperature are good examples.
Non-ohmic devices have resistance that varies with conditions:
- Tungsten filaments: Resistance increases substantially as they heat up (a cold lamp has much lower resistance than when glowing)
- Carbon arc: Resistance decreases as temperature increases (arc welding, arc lamps)
- Electrolytes: Resistance varies with concentration, temperature, and current density
- Diodes and transistors: Resistance depends on operating conditions
For non-ohmic devices, Ohm’s Law still applies instantaneously at any given moment—V = IR is always true—but R is not constant, so the relationship is not proportional over a range of conditions.
Practical Calculations
Designing a current-limiting resistor: An indicator LED requires exactly 20 mA (0.020A) and has 2V across it when conducting. Supply voltage is 12V. What series resistor is needed?
Voltage across resistor = 12V - 2V = 10V Required resistance = 10V / 0.020A = 500Ω Use the nearest standard value: 470Ω or 510Ω
Power dissipated in resistor = V × I = 10V × 0.020A = 0.2W → use a 0.5W resistor for safety margin
Calculating voltage drop on a wire: A 50-meter copper wire run (100 meters total for both conductors) carrying 10A of current. Wire is 2.5mm² cross-section copper (resistance ≈ 7.4Ω per kilometer).
Wire resistance = 7.4Ω/km × 0.1km = 0.74Ω Voltage drop = I × R = 10A × 0.74Ω = 7.4V For a 12V supply, this 7.4V drop is 62%—completely unacceptable. Use larger wire or higher voltage.
Battery internal resistance: A battery shows 12.6V open circuit. With a 2Ω load, terminal voltage drops to 11.8V. What is the internal resistance?
Current flowing = 11.8V / 2Ω = 5.9A Voltage drop across internal resistance = 12.6V - 11.8V = 0.8V Internal resistance = 0.8V / 5.9A = 0.136Ω
This internal resistance causes the battery to be inefficient under heavy load and to heat up. A higher internal resistance indicates an aging or damaged battery.
Power and Ohm’s Law Combined
Combining Ohm’s Law with the power formula P = V × I gives three equivalent power expressions:
- P = V × I (basic power formula)
- P = I² × R (heating effect; current squared times resistance)
- P = V² / R (voltage squared divided by resistance)
These allow power calculation when only two of the three quantities are known:
A wire carries 15A and has resistance 0.05Ω. What power does it dissipate as heat? P = I² × R = 225 × 0.05 = 11.25W — this wire is getting warm; check adequacy of gauge
A 100Ω resistor is connected across 12V. What power must it be rated for? P = V²/R = 144/100 = 1.44W → use a 2W rated resistor
A generator delivers 240V at 10A. What is its output power? P = V × I = 2,400W = 2.4 kW
Verifying Ohm’s Law Experimentally
This experiment can be performed with any battery, a set of resistors, and a galvanometer-based meter:
Equipment: Battery, variable resistor (rheostat), ammeter, voltmeter
Procedure:
- Connect battery to ammeter in series, with voltmeter connected across the external circuit
- Vary the rheostat resistance through several values
- Record V and I at each setting
- Calculate R = V/I at each setting
Expected result: R should be approximately constant for each rheostat setting, regardless of the exact current or voltage. Plot V on the vertical axis vs. I on the horizontal axis: the result should be a straight line through the origin, with slope = R.
A non-straight line indicates a non-ohmic element or a changing temperature affecting resistance.
Ohm’s Law in AC Circuits
In AC circuits, Ohm’s Law applies with an important extension. Inductors and capacitors present opposition to current that depends on frequency—called reactance (X). Combined resistance and reactance is called impedance (Z).
AC Ohm’s Law: V = I × Z
Where Z includes both resistance and reactance. For DC and low frequencies, reactance is negligible and Ohm’s Law simplifies to its DC form. At higher frequencies, reactance dominates and must be included.
For all practical power distribution work (DC systems, 50/60 Hz AC), the basic DC form of Ohm’s Law is adequate.
Limitations
Ohm’s Law is exact only for:
- Linear, ohmic materials
- Constant temperature conditions
- DC or low-frequency AC (where reactive effects are negligible)
It is a very close approximation for:
- Metal conductors at typical operating temperatures
- Circuit analysis at power frequencies
It does not apply directly to:
- Non-linear devices (diodes, transistors, thermistors)
- High-frequency circuits where inductive and capacitive effects are significant
- Superconductors (zero resistance, no voltage drop regardless of current)
Understanding these limitations ensures Ohm’s Law is applied where it is valid and supplemented with appropriate theory where it is not.