Verification of Ohm's law and series–parallel resistance
Verifying Ohm's law: circuit connections, tabular column, V–I graph, mean resistance against the colour-code value, why the ratio drifts when the resistor heats, and viva questions with answers.
Aim
To verify Ohm's law by measuring the current through a resistor at several applied voltages, and to confirm that the ratio V/I is constant and equal to the marked resistance within tolerance.
Apparatus required
| Apparatus | Specification | Qty |
|---|---|---|
| Regulated DC power supply | 0–30 V, 2 A | 1 |
| Resistor under test | 1 kΩ, ¼ W, ±5 % | 1 |
| Rheostat | For varying the applied voltage | 1 |
| Voltmeter (MC) | 0–10 V | 1 |
| Milliammeter (MC) | 0–25 mA | 1 |
| Digital multimeter | To check the colour-code value | 1 |
| Breadboard and patch cords | — | 1 set |
Theory
Ohm's law states that the current through a conductor is directly proportional to the potential difference across it, provided the physical conditions — above all the temperature — remain constant. The constant of proportionality is the resistance: V = IR.
The experiment tests that claim directly. If the law holds, doubling the applied voltage doubles the current, and every row of the table gives the same value of V/I. Plotted as V against I, the points lie on a straight line through the origin, and the slope of that line is the resistance.
The law is not universal. It describes ohmic conductors — metals and carbon resistors at constant temperature. A lamp filament, a diode, a thermistor and an electrolyte all give curved V–I plots, and for them resistance is not a single number.
The commonest way to see the law appear to fail is to let the resistor heat up. A quarter-watt resistor driven near its rating rises in temperature, and the resistance of most resistor materials rises with it, so V/I creeps upward through the readings. That drift is the experiment quietly demonstrating the 'constant temperature' clause.
The same circuit extends to series and parallel combinations: connect two known resistors in series and verify R = R₁ + R₂, then in parallel and verify 1/R = 1/R₁ + 1/R₂, each by the same V/I measurement.
Circuit connections
Check every point below against your board before switching on. There is no diagram here on purpose — a wrong diagram is worse than none, and this is the list a demonstrator actually walks through with you.
- Supply, rheostat, milliammeter and the resistor under test all in one series loop — the ammeter is always in series with the element whose current is being measured.
- Voltmeter directly across the resistor under test, in parallel — never in series.
- Observe polarity on both moving-coil meters: positive terminal towards the positive of the supply.
- Rheostat set for minimum output voltage before switching on.
Procedure
- 1Measure the resistor with the multimeter and read its colour bands. Record both values.
- 2Connect the circuit as above and have it checked, with the rheostat at minimum.
- 3Switch on and raise the voltage in equal steps. At each step record the voltmeter and milliammeter readings together.
- 4Take at least five or six readings, staying within the resistor's power rating — V²/R must stay below the rating.
- 5Switch off, and repeat the whole procedure for a series and then a parallel combination of two resistors if the experiment calls for it.
- 6Compute V/I for every row, take the mean, and compare it with the marked value. Plot V against I and confirm the straight line through the origin.
Work out your readings
Type in the numbers off the meters. This fills the tabular column, works the calculation through step by step, plots the characteristic — and tells you when a reading cannot physically be right, which is the part a manual can't do. Everything stays on this device, and it works with the network off.
Nameplate and machine data
Readings
Step the supply up in equal increments and read both meters at each step.
| # | Voltmeter V(V) | Ammeter I(mA) |
|---|---|---|
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 |
Fill in the machine data and at least one complete row of readings to see the results, the worked calculation and the curve.
Precautions
- The ammeter goes in series and the voltmeter in parallel. An ammeter across a supply is a short circuit.
- Check the power dissipated at the highest reading: a ¼ W resistor at 1 kΩ must not be taken past about 15 V.
- Set the rheostat to minimum before switching on, and raise the voltage gradually.
- Observe the polarity of moving-coil meters — connecting them backwards drives the pointer against the stop.
- Do not change the ammeter range part-way through without recording that you did; the multiplier changes with it.
Sources of error
Every record asks for these, and every record gets the same three lines copied from the one before. These are the errors this particular experiment actually has.
- Voltmeter loading: the voltmeter draws a small current that the ammeter also reads, so the measured current is slightly higher than the resistor's own. In this connection the error matters when the resistance is large.
- Self-heating of the resistor, which raises its resistance through the run and tilts the V–I line slightly.
- The ±5 % tolerance band of the resistor itself, before any measurement error is considered.
- Parallax and scale error on analogue meters, worst at the low end of the scale.
Viva questions with answers
State Ohm's law and its limitations.
The current through a conductor is directly proportional to the voltage across it, provided temperature and other physical conditions are constant. It applies only to ohmic (linear, bilateral) conductors — not to diodes, transistors, lamp filaments, thermistors or electrolytes.
Why must the temperature stay constant?
Because resistance depends on temperature. In metals it rises with temperature, so a resistor that heats during the experiment gives a slowly increasing V/I, and the V–I plot bends away from the straight line.
Why is an ammeter connected in series and a voltmeter in parallel?
An ammeter must carry the current it measures, so it goes in the path; it has very low resistance so it does not alter that current. A voltmeter must see the potential difference, so it goes across the element; it has very high resistance so it draws almost none of the current.
What is the slope of the V–I graph, and what does it mean if the line is curved?
The slope is the resistance. A curved line means the element is non-ohmic — its resistance depends on the current or voltage, as in a filament lamp or a diode.
How would you identify a 1 kΩ ±5 % resistor from its colour bands?
Brown–black–red for 10 × 10² = 1000 Ω, with a gold fourth band for ±5 %. On a five-band resistor it would be brown–black–black–brown with gold.
What is the difference between resistance and resistivity?
Resistance is a property of a particular object: R = ρL/A. Resistivity ρ is a property of the material alone, independent of size and shape, measured in ohm-metres.
In a series circuit, what is common — current or voltage?
Current. The same current flows through every element in series, and the applied voltage divides between them. In parallel it is the other way round: the voltage is common and the current divides.