Ohm's Law

Ohm’s law is one of the most useful relationships in electronics. It connects three quantities that appear in almost every circuit: voltage, current, and resistance. If you know any two of them, you can calculate the third—provided the component behaves approximately ohmically under the conditions being considered. This lesson builds the idea from practical intuition, then moves through the formula, units, worked examples, circuit measurements, common mistakes, and safe experiments. The aim is not simply to memorise V = IR, but to know when it applies and how to use it to make better design decisions.

1. What voltage, current, and resistance mean

Voltage is the difference in electric potential between two points. It describes the energy transferred per unit of charge. Voltage is measured in volts (V), and a measurement always compares two points; a voltage is not meaningfully measured at a single isolated point without a reference.

Current is the rate at which electric charge passes a point. It is measured in amperes (A). One ampere corresponds to one coulomb of charge passing per second. In a circuit diagram, conventional current is shown flowing from higher potential to lower potential through an external load, even though electrons in metal conductors drift in the opposite direction.

Resistance describes how strongly a component opposes current for a given voltage. It is measured in ohms (Ω). A resistor with a larger resistance draws less current than a smaller resistor when the same voltage is applied across it. Actual components may change resistance with temperature, voltage, illumination, or other conditions, so the simple model has limits.

A water analogy can help: pressure difference resembles voltage, flow rate resembles current, and a restriction resembles resistance. It is only an analogy. Electric circuits involve fields, charge carriers, and energy transfer, not water moving through a pipe.

2. The formula

Ohm’s law is commonly written as:

V = I × R

where V is voltage across the component in volts, I is current through it in amperes, and R is resistance in ohms. Rearranging gives:

• I = V / R — calculate current when voltage and resistance are known.
• R = V / I — calculate resistance from measured voltage and current, when current is non-zero.

Keep the units consistent. If resistance is written in kilohms (kΩ), convert it to ohms or use matching prefixes carefully. One kilohm is 1,000 ohms; one milliampere is 0.001 ampere. A frequent error is dividing volts by kilohms and reporting the result as amperes without accounting for the kilo-prefix. For example, 5 V across 1 kΩ produces 5 mA, not 5 A.

The formula relates voltage across a component to current through that same component. Do not use the supply voltage blindly if other components lie between the supply and the component being analysed. In a series circuit, the supply voltage is shared across the loads; in a parallel branch, each branch ideally has the same voltage as the source rails.

3. Worked examples

Example A: Find current. A 1 kΩ resistor is connected across a 5 V DC supply. Convert 1 kΩ to 1,000 Ω, then calculate I = V/R = 5/1,000 = 0.005 A = 5 mA. This is the ideal current through the resistor. In a real circuit, supply tolerance and resistor tolerance cause small differences.

Example B: Find voltage. A 220 Ω resistor carries 10 mA. Convert 10 mA to 0.010 A. Then V = IR = 0.010 × 220 = 2.2 V. This is the expected voltage drop across that resistor under those conditions.

Example C: Find resistance. A component has 3 V across it and carries 15 mA. R = V/I = 3/0.015 = 200 Ω. This calculation gives the ratio of voltage to current at that operating point. It does not prove that the component has a constant resistance at every operating point; an incandescent lamp, diode, or thermistor can behave non-linearly.

Example D: Estimate current before connecting a load. A nominal 9 V source is connected to a 3.3 kΩ resistor. I = 9/3,300 = 0.00273 A, or about 2.73 mA. If the resistor’s value is marked with a tolerance, calculate a range rather than treating the result as exact. A 5% resistor can be above or below its nominal value, changing the current correspondingly.

4. Ohm’s law in a simple circuit

Imagine a low-voltage DC source connected in series with a resistor. Current leaves the source’s positive terminal, passes through the resistor, and returns to the negative terminal in the conventional-current model. The same current flows through every element in a simple series path. The resistor has a voltage drop, and for an ideal resistor that drop follows V = IR.

For a 5 V source and a 1 kΩ resistor, the predicted current is 5 mA. If the resistor is changed to 2 kΩ while the supply remains at 5 V, the predicted current becomes 2.5 mA. Doubling resistance halves current at constant voltage. If resistance remains 1 kΩ and voltage falls from 5 V to 2.5 V, current also halves. These proportional relationships are the practical heart of the law.

Real supplies are not perfect. A battery has internal resistance, a bench supply may have current limiting, and wiring has some resistance. At higher currents, voltage drop in wires and connectors can matter. A microcontroller’s GPIO pin is not an ideal voltage source: it has current limits and a non-zero output resistance. Therefore, calculate the load current and check the component and board datasheets rather than assuming a GPIO pin can drive any load.

5. Choosing a resistor for an LED

A common beginner application is selecting a series resistor for an LED. The supply voltage is not usually dropped entirely across the resistor because the LED has a forward voltage. Estimate the resistor using R = (Vsupply − Vf) / ILED. This is an application of Ohm’s law to the resistor, not a claim that the LED itself obeys Ohm’s law.

For illustration, suppose a red LED has an assumed forward voltage of 2.0 V and you want 5 mA from a 5 V supply. The resistor voltage is approximately 5 − 2 = 3 V. R = 3/0.005 = 600 Ω. A nearby standard value such as 620 Ω gives a nominal current of about 4.8 mA under those assumptions. The actual forward voltage varies between LED parts and with current and temperature, so treat this as an estimate and check the LED datasheet.

Power in the resistor can be calculated as P = VI, or for a resistor, P = I²R and P = V²/R. In the example, P ≈ 3 V × 0.0048 A = 0.0144 W, or 14.4 mW. A typical 0.25 W resistor has ample nominal power margin for this low-current example, but designers should account for ambient temperature, enclosure conditions, and derating when appropriate.

Do not connect an LED directly across a voltage source without current limiting unless the specific circuit is designed to regulate its current. An LED can be damaged by excessive current even if it lights successfully at first.

6. Measuring voltage, current, and resistance

A digital multimeter measures voltage by being connected in parallel with the two points of interest. Choose a suitable DC-voltage range when measuring a DC circuit, and place the black lead in COM and the red lead in the voltage socket. Start with a range that safely covers the expected value if the meter is not auto-ranging.

Current measurement is different: the meter must be inserted in series so the circuit current passes through the meter’s current input. Move the red lead to the correct current socket, select the correct function and range, and observe the meter’s fuse and maximum-current ratings. Never place a meter configured for current measurement directly across a power supply; this can create a short circuit and may damage the meter, source, or wiring.

Resistance is measured with the circuit de-energised and the component isolated enough that parallel paths do not distort the reading. Never use resistance or continuity mode on a powered circuit. Capacitors may retain charge after power is removed; discharge them using an appropriate method and verify the voltage before measuring. If a reading seems inconsistent, check the meter mode, lead sockets, probe contact, circuit power, and whether other components are connected across the measurement points.

For beginner experiments, use a current-limited low-voltage supply or batteries and keep within the ratings of every part. Do not use a multimeter lesson as a reason to probe exposed mains wiring.

7. Where the simple law does—and does not—apply

A fixed resistor operating within its rated conditions is often well modelled by V = IR. The voltage-current graph is approximately a straight line through the origin, and its slope corresponds to resistance when voltage is plotted against current. This is the familiar ohmic behaviour.

A diode is different: current can change dramatically with a relatively small change in forward voltage, and the relationship is not a straight line. An LED is a diode. A thermistor changes resistance with temperature. An incandescent filament’s resistance changes as it heats. A transistor is a semiconductor device whose behaviour depends on its operating region and control terminal. For these components, V/I at one operating point can be calculated, but it may be misleading to treat that ratio as a constant resistance for all conditions.

Alternating current requires additional care. For a purely resistive element, instantaneous voltage and current follow the same proportional relationship, but inductors and capacitors introduce frequency-dependent impedance and phase differences. In AC circuits, the general relationship uses impedance rather than resistance alone. Do not apply a DC resistance calculation to a complex AC load without understanding the circuit model.

Datasheets matter because a resistor can overheat if power exceeds its rating, and semiconductor current and voltage limits are not recommendations to operate at the maximum continuously. Ohm’s law is a foundational tool, not a substitute for component specifications or circuit analysis.

8. Common mistakes and a troubleshooting checklist

Mixing units: convert milliamperes to amperes when using the standard formula. For instance, 20 mA is 0.020 A. Using the wrong voltage: use the voltage across the component being analysed, not automatically the source voltage. Ignoring series parts: an LED and its resistor share the supply voltage. Assuming all parts are ohmic: the law does not make a diode or motor a fixed resistor. Forgetting power: a calculated current can still overheat a component. Measuring current in parallel: this is a serious meter-use error that can short the source.

When a measured current differs from a calculation, work systematically. Confirm the resistor value and tolerance, measure the actual supply voltage, inspect the wiring, and verify the meter range and lead placement. Consider whether the supply is current-limiting or sagging under load. For a semiconductor circuit, compare the expected operating point with the datasheet rather than forcing the result to fit a resistor-only model.

A useful habit is to write down the known values with units before calculating. Estimate the order of magnitude first: a few volts across a few thousand ohms should normally produce milliamperes, not tens of amperes. Then check whether the answer is physically plausible and whether component power ratings are respected.

9. Practice questions

Try these before checking the answers. 1. What current flows through 470 Ω connected to 9 V? 2. What voltage appears across a 330 Ω resistor carrying 12 mA? 3. A load draws 25 mA from 5 V. What is its V/I ratio at that operating point? 4. A resistor has 4 V across it and carries 20 mA. What power does it dissipate? 5. Why is a multimeter in current mode not connected across a supply?

Answers: 1. I = 9/470 ≈ 0.0191 A, or 19.1 mA. 2. V = 0.012 × 330 = 3.96 V. 3. R-equivalent = 5/0.025 = 200 Ω at that operating point; this does not prove the load is a fixed resistor. 4. P = VI = 4 × 0.020 = 0.08 W, or 80 mW; select a resistor rating with suitable margin. 5. The meter’s current input has very low resistance, so placing it across the source can create a near-short circuit and cause excessive current.

For a hands-on low-voltage exercise, predict the current through a 1 kΩ resistor at 3 V, 4.5 V, and 5 V. Then measure the circuit using a correctly configured multimeter and compare results. Switch off the circuit before changing wiring, keep the resistor within its power rating, and record both the predicted and measured values. The difference is an opportunity to learn about tolerances and measurement uncertainty, not automatically evidence that the law is wrong.

10. Key takeaways and what to learn next

Ohm’s law connects voltage, current, and resistance through V = IR. Use I = V/R to estimate current, V = IR to calculate a voltage drop, and R = V/I to find the ratio at a measured operating point. Keep units consistent, use the voltage across the part in question, and check power as well as current. Remember that real components have tolerances and operating limits, and that non-ohmic devices cannot always be represented by one fixed resistance.

To build on this lesson, study Voltage, Current, Resistance, and Power as related concepts, then move to Series Circuit and Parallel Circuit to see how voltage and current behave across multiple components. Reading Resistors helps you identify component values, while Using a Multimeter covers practical measurement technique. When experimenting with Arduino or ESP32 boards, use current-limiting resistors for LEDs and check the board’s GPIO specifications. SolderHub’s goal is to connect the underlying theory to practical builds: calculate first, wire carefully, measure, and compare your observations with the model.

Accuracy note: worked examples use idealised values for teaching. Actual results depend on supply voltage, component tolerance, temperature, meter accuracy, and the operating characteristics described in the relevant datasheets.