Aim and apparatus
Aim
To verify Ohm's law, that is, to study how the current through a conductor depends on the potential difference across it, and to find the resistance of a wire from the slope of its V–I graph.
Apparatus in this virtual lab
- DC power supply, 0–12 V, with a 1.5 A current limit
- Rheostat, 0–50 Ω
- Digital ammeter (connected in series)
- Digital voltmeter (connected across the test wire)
- Test wire on a metre scale with a sliding contact (jockey): nichrome, constantan or copper, 20–100 cm long, 0.2, 0.3 or 0.5 mm thick
- Connecting wires
Theory
Ohm's law
At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends.
R is the resistance of the conductor, measured in ohm (Ω). A graph of V against I is a straight line through the origin, and its slope is R.
What decides resistance
Resistance grows with length L and with the resistivity ρ of the material, and falls as the cross-section area A grows. Thicker wire means lower resistance.
| Material | ρ at about 25 °C | Temperature coefficient α |
|---|---|---|
| Nichrome | \(1.10\times10^{-6}\ \Omega\,\mathrm{m}\) | \(4\times10^{-4}\ ^\circ\mathrm{C}^{-1}\) |
| Constantan | \(4.9\times10^{-7}\ \Omega\,\mathrm{m}\) | \(\approx10^{-5}\ ^\circ\mathrm{C}^{-1}\) |
| Copper | \(1.68\times10^{-8}\ \Omega\,\mathrm{m}\) | \(3.9\times10^{-3}\ ^\circ\mathrm{C}^{-1}\) |
Why temperature matters
When current flows, the wire heats up with power \(P=I^{2}R\). Resistance then rises with temperature:
If the wire gets hot, V ÷ I is no longer constant and the V–I graph bends. That is why Ohm's law is stated "at constant temperature". Constantan has almost no change, which is why it is used in resistance boxes.
The circuit
The rheostat, ammeter and test wire are connected in series with the power supply. The voltmeter is connected in parallel across the test wire. The rheostat changes the current, and the whiteboard in the lab shows the circuit diagram with the standard symbols.
Resistors in series and in parallel
In series the same current flows through each wire, and the p.d.s add up: \(V = V_1 + V_2\). The total resistance is the sum:
In parallel the p.d. across each wire is the same and the currents add up: \(I = I_1 + I_2\). The total resistance is less than either wire:
Two equal wires in series have twice the resistance of one; in parallel, half. Try both in More to explore.
I–V graphs of other components
- Metal wire at constant temperature: a straight line through the origin; it obeys Ohm's law (it is ohmic).
- Filament lamp: the graph curves. As the current increases, the filament gets hotter and its resistance increases, so V ÷ I gets bigger.
- Diode: almost no current flows until the p.d. reaches about 0.6 V, then the current rises steeply. Reversed, it lets (almost) no current through: a diode lets current flow in one direction only.
Use Reverse the supply to see the negative half of each graph: the wire and the lamp give the same shape upside down; the diode gives zero current.
How to use this virtual lab
- Look at the setup. The whiteboard shows the circuit. On the bench, left to right, are the supply, rheostat, ammeter, test wire and voltmeter.
- Switch on the power supply using the toggle at the top of the left panel. The meters come alive and blue dots show the current flowing from + to −.
- Choose the wire. Pick the material, then set length and thickness. Each combination gets its own observation table. The jockey on the scale moves as you change length.
- Set the supply voltage (for example 6 V) and move the rheostat to its largest value, so that you start with the smallest current.
- Read the meters and press Record reading. The voltmeter and ammeter values are copied into the Observations table.
- Reduce the rheostat in steps (for example 40, 30, 20, 10 Ω) and record each time. Take at least five readings. You can also record a (0, 0) reading with the supply set to 0 V.
- Open Data & graph and look at your table, then press Plot data. The graph shows your points and a best-fit line through the origin. The slope is the resistance R, shown next to the value \(\rho L/A\) for comparison.
- Compare wires. Change the wire and repeat. Plotted wires stay on the same graph, and the chips above the table take you back to an earlier wire.
- Explore the temperature effect. Turn on "Let the wire heat up", raise the current, and watch the wire glow. Switch the graph to Join points to see the line curve.
- More to explore (bottom of the left panel): connect a second wire in series or parallel (and choose where the voltmeter goes), replace the wire with a filament lamp or a diode, and reverse the supply. Each one gets its own table and line on the graph, with the theoretical resistance for comparison.
- Use full screen for a bigger lab with scroll-wheel zoom. The Front view button always brings the camera back to the starting position.
Controls at a glance
| Control | What it does |
|---|---|
| Power supply switch | Turns the circuit on or off. The status badge shows Running, Wire heating or Current limit. |
| Wire under test | Material, length and thickness of the wire. These decide its resistance through \(R=\rho L/A\). |
| Supply voltage | Sets the output of the DC supply from 0 to 12 V. |
| Rheostat | Adds 0 to 50 Ω in series. More resistance means less current. |
| Let the wire heat up | Off keeps the wire at 25 °C. On lets it heat from \(I^{2}R\) so that its resistance can change. |
| More to explore | Two wires (series or parallel, with the voltmeter across both or one wire), a filament lamp or a diode instead of the wire, and a switch to reverse the supply. |
| Record reading | Stores the current voltmeter and ammeter values in the table. |
| Plot data | Draws the V–I graph for the wire you are working on. |
| Best-fit line / Join points | Straight line through the origin with slope R, or the recorded points joined to show the real shape. |
| Front view | Resets the camera to the front of the lab. |
Observations and calculations
Observation table
Record at least five readings for each wire. The lab fills this table for you.
| S.No. | V (volt) | I (ampere) | V ÷ I (Ω) |
|---|---|---|---|
| 1 | … | … | … |
| 2 | … | … | … |
| 3 | … | … | … |
Calculations
Result
The V–I graph is a straight line through the origin, so the potential difference across the wire is proportional to the current through it, and Ohm's law is verified. The resistance of the wire is the slope of the graph.
Sources of error
- Heating of the wire raises its resistance
- Contact resistance at the terminals and the jockey
- Error in reading the length of the wire from the scale
- Limited precision of the meters
Precautions
- Connect the ammeter in series and the voltmeter in parallel, with the + terminal towards the positive side of the supply.
- Keep the current small so that the wire does not heat up. In a real lab, switch the circuit off between readings.
- Make sure all connections are tight and the wire ends are clean.
- Check that both meters read zero before the circuit is switched on.
- Take readings only after the meter values have settled.
Exam practice
Questions like the ones asked in board practical exams and theory papers. Try each one before opening the answer.
Why does the V–I line pass through the origin?
If there is no potential difference there is no current, so \(V=0\) when \(I=0\). For an ohmic conductor \(V=IR\) has no constant term.
Why is a rheostat used?
It changes the resistance of the circuit and so changes the current, which lets you take many pairs of readings. It also protects the meters from a large current.
Why is the voltmeter connected in parallel?
It must measure the potential difference across the wire, so it is connected across it. It has a very high resistance so that it takes almost no current.
What does the slope of the V–I graph represent? What about the I–V graph?
The slope of V against I is the resistance R. The slope of I against V is \(1/R\), the conductance.
Do all conductors obey Ohm's law?
No. Metallic wires at constant temperature do. A filament lamp, a diode or a thermistor do not, because their resistance changes with current or temperature.
Why is constantan used for standard resistors?
Its resistance hardly changes with temperature, so its resistance stays steady even when it warms up.
What does the "Current limit" badge mean?
The supply cannot give more than 1.5 A. If the circuit would need more, the supply holds the current at 1.5 A instead and the voltage across the circuit drops.
Two identical wires of 9.3 Ω each are connected first in series, then in parallel. What is the total resistance each time?
Series: \(R = 9.3 + 9.3 = 18.6\ \Omega\). Parallel: \(R = \dfrac{9.3\times 9.3}{9.3+9.3} = 4.65\ \Omega\), half of one wire.
Why is the total resistance of two resistors in parallel less than either one?
Connecting a second resistor in parallel gives the current an extra path, so for the same p.d. more current flows. More current for the same p.d. means less resistance.
Sketch and explain the I–V graph of a filament lamp.
It is a curve through the origin that bends: as the p.d. increases, the current increases by less and less. The filament gets hotter as the current increases, and the resistance of a metal increases with temperature.
Describe the I–V graph of a diode and state what a diode is used for.
Almost no current flows in the reverse direction, or in the forward direction below about 0.6 V; above that, the current rises steeply. A diode lets current flow in one direction only, so it is used to protect circuits and to change a.c. into d.c. (rectification).