The Ohm’s law experiment is a basic electrical experiment in which the relationship between the voltage applied to a conductor and the current flowing through it is measured to confirm that voltage is proportional to current.
For a resistor under constant conditions such as temperature, increasing the voltage across it causes the current to increase proportionally. This proportional relationship is called Ohm’s law, and the relationship among voltage, current, and resistance is expressed as V = RI.
In the experiment, a DC power supply, resistor, ammeter, and voltmeter are connected, and the current is measured while the voltage is changed step by step. When the measured values are plotted, a resistor that obeys Ohm’s law produces a straight line passing near the origin.
This article assumes a DC circuit measurement using a fixed resistor and presents an introduction, precautions, items to record, sample experimental values, calculations, sources of error, an example results section, and discussion examples.
Note:
This article is a study reference for discussing results obtained in physics experiments at schools, universities, and similar institutions. The experimental values shown are illustrative examples and are not actual measurement results.
Always turn off the power before changing the wiring. Short-circuiting the power supply, exceeding the resistor’s rated power, or connecting an ammeter in parallel can damage equipment or cause overheating. Follow the instructions in your school’s laboratory manual and those of your instructor or TA.
Ohm’s Law
If the voltage across a resistor is V, the current through it is I, and its resistance is R, the following relationship holds when conditions such as temperature remain constant.
V = RI
Rearranging this equation gives the current and resistance as follows.
I = V/R
R = V/I
Voltage-Current Graph
When current I is plotted on the horizontal axis and voltage V on the vertical axis, a resistor obeying Ohm’s law gives a straight line whose slope represents the resistance.
Slope = ΔV/ΔI = R
If voltage is on the horizontal axis and current on the vertical axis, the slope is 1/R. Care must be taken not to confuse the graph axes.
Power and Heating
The power consumed by a resistor is expressed as follows.
P = VI = I2R = V2/R
As current increases, heating increases and the resistor temperature may rise. In metallic resistors, resistance generally increases with temperature, so the measurements may deviate from a perfectly straight line at higher voltages.
Main Items to Record in the Results
- Nominal resistance of the resistor
- Resistor tolerance
- Rated power of the resistor
- Range of the DC power supply used
- Measurement ranges of the voltmeter and ammeter
- Smallest scale division or resolution of the voltmeter and ammeter
- Voltage at each measurement point
- Current at each measurement point
- Resistance calculated at each measurement point
- Voltage-current graph
- Slope of the best-fit line
- Resistance obtained from the graph
- Relative error from the nominal value
- Power consumption at each measurement point
- Measurements when increasing and decreasing the voltage
- Any temperature change or heating of the resistor
Sample Experimental Conditions
| Item | Sample Condition |
|---|---|
| Resistor | 100 Ω |
| Tolerance | ±5% |
| Rated power | 0.5 W |
| DC power supply | 0–6 V |
| Voltmeter | Digital voltmeter |
| Ammeter | Digital ammeter |
| Measurement interval | 0.5 V |
| Room temperature during measurement | 23 ℃ |
Sample Experimental Values
Example Voltage and Current Measurements
| Measurement No. | Voltage V (V) | Current I (mA) | Resistance R = V/I (Ω) | Power P (W) |
|---|---|---|---|---|
| 1 | 0.50 | 4.98 | 100.4 | 0.0025 |
| 2 | 1.00 | 9.96 | 100.4 | 0.0100 |
| 3 | 1.50 | 14.93 | 100.5 | 0.0224 |
| 4 | 2.00 | 19.90 | 100.5 | 0.0398 |
| 5 | 2.50 | 24.85 | 100.6 | 0.0621 |
| 6 | 3.00 | 29.80 | 100.7 | 0.0894 |
| 7 | 3.50 | 34.72 | 100.8 | 0.1215 |
| 8 | 4.00 | 39.60 | 101.0 | 0.1584 |
| 9 | 4.50 | 44.45 | 101.2 | 0.2000 |
| 10 | 5.00 | 49.25 | 101.5 | 0.2463 |
The current increases almost proportionally as the voltage increases. However, the resistance becomes slightly larger at higher voltages, possibly because of a temperature rise caused by resistor heating.
Example Repeated Measurements
| Voltage | 1st (mA) | 2nd (mA) | 3rd (mA) | Average Current (mA) |
|---|---|---|---|---|
| 1.0 V | 9.95 | 9.97 | 9.96 | 9.96 |
| 2.0 V | 19.88 | 19.91 | 19.90 | 19.90 |
| 3.0 V | 29.78 | 29.81 | 29.80 | 29.80 |
| 4.0 V | 39.58 | 39.61 | 39.60 | 39.60 |
| 5.0 V | 49.22 | 49.27 | 49.25 | 49.25 |
Comparison of Different Resistors
| Nominal Resistance | Current at 3.00 V | Resistance Obtained Experimentally | Graph Feature |
|---|---|---|---|
| 50 Ω | 59.6 mA | 50.3 Ω | Smaller slope |
| 100 Ω | 29.8 mA | 100.7 Ω | Intermediate |
| 220 Ω | 13.6 mA | 220.6 Ω | Larger slope |
When voltage is plotted vertically and current horizontally, a larger resistance produces a steeper line.
Calculation Methods
Calculating Resistance from One Measurement
For a voltage of 3.00 V and a current of 29.80 mA, first convert the current to amperes.
I = 29.80 mA = 0.02980 A
R = V/I
= 3.00 / 0.02980
= 100.7 Ω
Calculating Resistance from the Graph Slope
For example, if two points on the best-fit line are (10.0 mA, 1.01 V) and (40.0 mA, 4.03 V), the calculation is as follows.
R = ΔV/ΔI
= (4.03 − 1.01) / {(40.0 − 10.0) × 10−3}
= 3.02 / 0.0300
= 100.7 Ω
Average Resistance
If the measured resistance values are 100.4 Ω, 100.5 Ω, 100.7 Ω, 101.0 Ω, and 101.5 Ω:
Average resistance = (100.4 + 100.5 + 100.7 + 101.0 + 101.5) / 5
= 100.82 Ω
Relative Error from the Nominal Value
For an experimental value of 100.7 Ω and a nominal value of 100 Ω:
Relative error (%) = |Experimental value − Nominal value| / Nominal value × 100
= |100.7 − 100| / 100 × 100
= 0.7%
Resistor Tolerance Range
For a 100 Ω resistor with a tolerance of ±5%, the acceptable range is:
Lower limit = 100 × (1 − 0.05) = 95 Ω
Upper limit = 100 × (1 + 0.05) = 105 Ω
The experimental value of 100.7 Ω is within this tolerance range.
Power Consumption
For a voltage of 5.00 V and a current of 49.25 mA:
P = VI
= 5.00 × 0.04925
= 0.246 W
Because the resistor is rated at 0.5 W, this measurement is within its rating, although prolonged current flow may still cause a temperature rise.
Approximate Maximum Applied Voltage
For a resistance of 100 Ω and a rated power of 0.5 W, the theoretical maximum voltage that does not exceed the power rating is:
V = √(PR)
= √(0.5 × 100)
= approximately 7.07 V
In practice, a safety margin should be maintained and prolonged operation near the rated limit should be avoided.
Main Sources of Error
| Source of Error | Effect on Measurement | Likely Trend in Results | Improvement |
|---|---|---|---|
| Resistor heating | Resistance changes as temperature rises | Current becomes smaller than the theoretical value at high voltage | Measure quickly and allow cooling between measurements |
| Resistor tolerance | Actual resistance differs from nominal value | A constant percentage difference appears at all measurement points | Measure the actual resistance with a multimeter beforehand |
| Internal resistance of ammeter | Increases total circuit resistance | Current is smaller than the ideal value | Use an ammeter with low internal resistance |
| Internal resistance of voltmeter | A small current also flows through the voltmeter | May affect current measurement depending on connection method | Use a voltmeter with high internal resistance |
| Wire and contact resistance | Voltage drops occur outside the resistor | Calculated resistance becomes larger | Use short wires and secure connections |
| Power-supply voltage fluctuations | Voltage changes during measurement | Current varies even at the same setting | Read the actual voltage at every measurement |
| Instrument zero error | Adds a constant offset to all measurements | Graph does not pass through the origin | Check and correct zero before measurement |
| Instrument resolution | Small changes cannot be resolved | Relative error is larger at low voltage | Select an appropriate measurement range |
| Parallax in reading | Analog pointer is viewed at an angle | Voltage and current values shift irregularly | Read perpendicular to the scale |
| Incorrect ammeter/voltmeter connection | Correct current or voltage cannot be measured | Abnormal values or instrument overload | Connect the ammeter in series and voltmeter in parallel |
| Poor contact | Contact resistance changes over time | Measurements are unstable | Clean and firmly secure clips and terminals |
| Choice of best-fit line | Slope is calculated from only some points | Resistance depends on which points are chosen | Use least-squares fitting with all measurement points |
Why Voltage and Current Are Proportional
In a metallic conductor at constant temperature, a stronger electric field exerts a larger force on free electrons and increases their average drift velocity. As a result, current increases in proportion to voltage.
Inside the conductor, electrons are scattered by effects such as thermal vibrations of atoms, and this opposition to their motion appears as electrical resistance.
Why the Graph Slope Equals Resistance
Ohm’s law, V = RI, has the same form as the straight-line equation y = ax when voltage is plotted vertically and current horizontally.
Therefore, the proportionality constant corresponding to the slope is the resistance R.
Why the Graph May Deviate at High Voltage
Increasing the voltage increases the current and therefore the power dissipated in the resistor. If heating raises the resistor temperature, the resistance of a metallic resistor generally increases.
Consequently, at higher voltages the current may become smaller than predicted by a simple proportional relationship, causing the graph to curve slightly.
Why the Graph May Not Pass Through the Origin
For an ideal resistor, zero voltage means zero current. In an experiment, however, instrument zero error, residual power-supply voltage, measurement resolution, and fitting error can prevent the graph from passing exactly through the origin.
Why the Ammeter Is Connected in Series and the Voltmeter in Parallel
An ammeter must carry the same current as the component being measured, so it is connected in series with the circuit. Ideally, an ammeter has zero internal resistance.
A voltmeter measures the potential difference across a component, so it is connected in parallel with it. Ideally, a voltmeter has infinite internal resistance.
Example of Writing the Results
A DC voltage of 0.50–5.00 V was applied to a resistor with a nominal resistance of 100 Ω, and the current at each voltage was measured.
The current was 4.98 mA at 0.50 V, 29.80 mA at 3.00 V, and 49.25 mA at 5.00 V, increasing almost proportionally with voltage.
With voltage on the vertical axis and current on the horizontal axis, a best-fit line gave a resistance of 100.7 Ω from its slope. The relative error from the nominal value of 100 Ω was 0.7%, which was within the resistor’s ±5% tolerance.
Points to Connect to the Discussion
- Were voltage and current proportional?
- Was the V-I graph a straight line passing near the origin?
- What resistance was obtained from the graph slope?
- Was V/I constant at each measurement point?
- Was the experimental value within the resistor tolerance?
- Did resistance change at higher voltages?
- How did resistor heating affect the results?
- How did the internal resistance of the ammeter and voltmeter affect the measurements?
- Could wire resistance and contact resistance be neglected?
- Why might the graph fail to pass through the origin?
- Why is using the graph slope preferable to calculating V/I from one point?
Discussion Example
In this experiment, the DC voltage applied to a resistor with a nominal resistance of 100 Ω was changed step by step, and the current through the resistor was measured to verify Ohm’s law.
As the voltage increased from 0.50 V to 5.00 V, the current increased almost proportionally from 4.98 mA to 49.25 mA. A plot with voltage on the vertical axis and current on the horizontal axis placed the measurement points approximately on a straight line passing near the origin.
The resistance obtained from the slope of the best-fit line was 100.7 Ω. This was 0.7% higher than the nominal value of 100 Ω but remained within the 95–105 Ω range specified by the resistor’s ±5% tolerance.
Calculating R = V/I at each measurement point gave approximately 100.4 Ω at low voltage and approximately 101.5 Ω at high voltage. The resistance was nearly constant overall, indicating that Ohm’s law held under the experimental conditions.
However, the resistance showed a slight tendency to increase at higher voltages. At 5.00 V, the power consumption was approximately 0.246 W, producing more heating than at lower voltages. As the temperature of a metallic conductor rises, atomic thermal vibrations increase and electrons are scattered more strongly, which may have increased the resistance.
Possible sources of measurement error include the resistor’s own tolerance, the internal resistance of the ammeter and voltmeter, wire and contact resistance, fluctuations in the power-supply voltage, and instrument resolution.
Because an ammeter has a small but finite internal resistance, connecting it in series slightly increases the total circuit resistance. This can make the measured current smaller than the ideal value and cause the calculated resistance to be larger.
The voltmeter also has finite internal resistance, so a small current flows through it. Depending on where the ammeter is connected, the measured current may include not only the current through the resistor but also the current through the voltmeter.
Wires and contacts also have small resistances. In particular, loose terminals can increase contact resistance and may cause it to change during measurement.
When resistance is calculated from V/I at a single measurement point, the reading error at that point directly affects the result. In contrast, finding the slope of a best-fit line using multiple measurements averages random errors and provides a more reliable resistance value.
If the graph does not pass exactly through the origin, possible causes include instrument zero error, residual power-supply voltage, measurement resolution, and uncertainty in fitting the line. If the intercept is small compared with the measurement uncertainty, the result is not inconsistent with Ohm’s law.
To improve accuracy, the voltage should not be raised excessively, and each measurement should be made quickly to limit resistor heating. The actual resistor value should also be checked before measurement, an appropriate instrument range should be selected, and all terminals should be securely connected.
Therefore, within the range where the resistor temperature remained approximately constant, voltage and current were proportional and resistance remained nearly constant, confirming Ohm’s law.
Discussion Example When the Measured Resistance Is Higher Than the Nominal Value
Possible reasons why the measured resistance was higher than the nominal value include component-to-component variation, resistor heating, the internal resistance of the ammeter, and the resistance of wires and contacts. If the difference from the nominal value is within the resistor’s specified tolerance, the measurement is consistent with the component specification.
Discussion Example When the Graph Curves at High Voltage
If the current at high voltage is smaller than expected from the proportional relationship, an increase in resistance due to resistor heating is a possible cause. Because power consumption increases with the square of voltage, temperature-rise effects become larger at higher voltages.
Discussion Example When the Graph Does Not Pass Through the Origin
Possible reasons why the best-fit line did not pass through the origin include zero error in the ammeter or voltmeter, residual output from the power supply, and insufficient measurement resolution in the low-voltage range. If the intercept is comparable to the instrument uncertainty, the graph can effectively be regarded as passing through the origin.
Summary
In an Ohm’s law experiment, the voltage applied to a resistor and the current through it are measured to confirm that they are proportional.
When voltage is plotted vertically and current horizontally, the slope of the graph represents resistance. Resistance remains approximately constant when temperature is constant, but it may change at higher voltages because of heating.
In the discussion, it is important to relate the V-I graph, resistance, tolerance, power consumption, resistor heating, instrument internal resistance, wire resistance, and zero error to one another.
