Tag Archive for: resistance

Force on a Current-Carrying Wire

A-Level Physics Required Practicals:
Force on a Current-Carrying Wire

Supporting notes for this film will follow shortly.

Assessment

— to follow

Student Worksheet

— to follow

Comments & Feedback

As ever, no single film can encompass everything one might wish to say about a practical. Please, leave comments with your thoughts about the approach we’ve taken, and your suggestions for alternatives or improvements.


Discharging a Capacitor

A-Level Physics Required Practicals:
Investigating the Discharge of a Capacitor

All the new specifications include a required practical that asks students to investigate capacitors charging or discharging through a resistor. The awarding bodies agree that this practical is an ideal opportunity for students to develop their skills in using ICT.

What’s in the Film

It’s possible to measure the changing potential difference across the capacitor using:

  • A voltmeter and stopwatch.
  • An oscilloscope (whether cathode ray or digital, for example a Picoscope).
  • A datalogger.

The circuit will be similar whichever approach you use. A meter connected in parallel across the resistor R measures V. With the switch connected at A, the capacitor C charges (almost instantly, since there is negligible resistance in the circuit). When the switch is flicked to position B the capacitor discharges through the resistor, with both the current and voltage decreasing exponentially.

In their experiments, both Alom and Carol do without a two-way switch and instead simply disconnect the capacitor from the power supply to make it discharge through the resistor.

As Alom mentions in the introduction, the uses of capacitors are quite interesting for giving the students some context here. He refers to a previous film:


The Datalogger Method

In core practical film, Alom uses Edu-lab data loggers (see below for approximate costings), but there are many alternatives. You could also use a digital oscilloscope which stores data, or a computer-based ‘Picoscope’ or similar which functions equivalently.



From 1’32” in the film Alom suggests that students can check the discharge curve is exponential by seeing if there is a constant half-life (the time taken for the potential difference to fall by a half). Or, better, to measure the time constant and if it that is… er… constant (the time constant is the time taken for the measured potential difference to drop to 1/e of its original value – see the graph above).

Earlier in the film, Alom chooses values for and R which multiply to give a time constant which is measurable: neither too fast nor too slow. In this case:

\(C = 4700~\mathrm{\mu F}\)
\(R = 10~\mathrm{k\Omega}\)
So time constant \(\tau = 4700\times10^{-6} \cdot 10 \cdot 10^3 = 47~\mathrm{s}\)

The exponential equation:

\(V = V_{0}e^{-t/RC}\)

is one which students will need to be able to handle. Alom shows how to manipulate this into the form of a straight-line graph. First, take natural logs of both sides:

\(ln(V) = ln(V_0) – \frac{t}{RC}\)

Compare with:

\(y = mx + c\)

If \(ln(V)\) is plotted on the y-axis against \(t\) on the x-axis, then \(ln(V_0)\) will be the y-intercept and \(-\frac{1}{RC}\) the gradient, hence \(C\) if \(R\) is known.


Resistor colour code

This might be a useful opportunity to show students the resistor colour code:

Questions

You might like to ask your students:

  • Why is a datalogging method appropriate for this practical?
  • Does it matter which way round we connect the capacitor? (see Carol’s comment at 3’21).
  • For how long should we time the discharge?
  • What would happen if we instead measured V while the capacitor charges?
  • Why process the data so we get a straight line graph? Why is this better than a curve?
  • What should the units of \(ln(V)\) be?

The Direct Measurement Method

Carol uses a multimeter as a voltmeter and a stopclock to do the timing manually. She suggests measuring V every ten seconds: it’s hard to record it any more frequently, but take less frequent measurements and the graph will be hard to draw, with too few data points. Any voltmeter will do: digital, analogue, multimeter, or even an oscilloscope.

Students could be challenged to find an unknown capacitance by measuring the time constant obtained with a particular resistor. In the film, Carol explains that some preliminary runs will be needed to test the circuit and to ensure they have a suitably measurable time constant.

This method lends itself to the use of ICT, in that students can put their data into a spreadsheet and manipulate them into a straight line for (as shown above). Alternatively, data can be processed by hand.

You might as your students:

  • Why do we not need to worry about starting the timing immediately the discharge begins? (This will test their understanding of the exponential decay function.)
  • What are the causes of uncertainty in the experiment – not only our measurements, but the manufacturers’ tolerances for their components?
  • How can we reduce the uncertainty in our readings?

Safety

Since \(Q = CV\), a large capacitor charged to a huge voltage stores a lot of charge, which will lead to a high initial charging or discharging current, with consequent heating effect. The values used in the film (and noted above) offer a good guide to what works well – and safely.

Capacitors should not be charged to a voltage higher than that stated on their labelling or product information sheets. Electrolytic capacitors should be connected with the correct polarity.

It’s also important to ensure the capacitor is discharged before touching it: disconnect the power, then operate the circuit to discharge the capacitor through the resistance before dismantling the apparatus.

Costs

The Edu-logger system used in the film sells for around:

  • £45 for the voltage sensor
  • £43 for the USB module to connect to a PC (standalone display/tablet/smartphone alternatives are available).
  • £43 for a battery module.

Those figures are without VAT. Other systems are available for similar prices, or you can spend considerably more on systems with increasing levels of flexibility. Most suppliers will offer discounts on bulk orders.

Further work

The IOP’s Teaching Advanced Physics website has a series of articles about teaching topics around capacitance:

Assessment

Common Practical Assessment Criteria

At the time of writing, the exam boards appear to agree that this practical might be used to address, in whole or in part:

  • CPAC 3: Safely use a range of practical equipment and materials.
  • CPAC 4: Makes and records observations.

Student Worksheet

We’ve drafted a student worksheet for this practical, which you may find useful as a starting point:

Comments & Feedback

As ever, no single film can encompass everything one might wish to say about a practical. Please, leave comments with your thoughts about the approach we’ve taken, and your suggestions for alternatives or improvements.


Measuring the EMF and Internal Resistance of a Cell

A-Level Physics Required Practicals:
Measuring the EMF and Internal Resistance of a Cell

All the new specifications include “measure the internal resistance of a cell” as one of the practicals. This is probably a new bit of physics for your students, and although the practical is straightforward to set up, collecting and processing the data is more of a challenge. Comparing two different types of cell, as shown in this film, can make the practical more interesting, with potential for differentiation by ability.

What’s in the Film

The film starts (to 1:24) with the theory which you’ll probably introduce to students before carrying out the practical.

From 1:30 onwards, the film illustrates how you might go about conducting the practical with conventional cells, and also with a button cell (watch battery).

Safety

Christina and Alom do several things in the film to limit the current so the cell doesn’t overheat: they use a limiting resistor, start with low currents, and connect the circuit only momentarily. This represents safe working practice, but heating the cell would also affect the resistance we’re trying to measure.


AA Cell


We used a 10 Ω resistor to limit the current in the circuit. A simple fixed resistor would do, but make sure it can handle the maximum power you expect in the circuit – a few Watts. We didn’t have such a resistor to hand for filming, hence the huge switchable resistance box.

To vary the current to get multiple readings we used an old rheostat, rated at about 16 Ω. In practice anything with a range up to 50 Ω or so should work. It’s also possible to use a range of different fixed resistors, or a switchable resistance box.

Digital or analogue voltmeters or ammeters could be used instead of multimeters, but as Christina points out in the film, the use of multimeters is a skill your students will need to develop anyway. Students will need to select the most appropriate range, which is likely to be 20 V DC for the voltmeter and 200 mA DC for the ammeter (taking care to convert back to amps when processing the data).

Alom’s multimeter films may be dull, but they’ve had a third of a million views so… they may have some redeeming merit. Click through to YouTube or to maximise the film from these tiny windows:

Measuring Voltage with a Multimeter


Measuring Current with a Multimeter


Collecting & Processing Data


Working in pairs, this experiment can be be done very quickly. Systematic data are nice, but as long as there’s a good spread of data points across the whole range of currents, students should get a good result.



From our data, we arrived at:

Gradient = -2.10
y-intercept = 1.415

so:

EMF = 1.415 V
Internal resistance = 2.10 Ω

We would normally expect an AA cell to have an EMF of about 1.5 V and an internal resistance of about 1 Ω. Ours was old and cheap, which probably explains our results: it’s worth noting that poorer-quality cells can make for a more interesting experiment!

You might ask your students:

  • Is their result what they would expect from the cell packaging or label?
  • How could they assess the uncertainty in their data?

Christina mentions tolerance at 4’11”, which is a concept with which students may not be familiar. All components have a stated manufacturer’s tolerance, which notes the ±% range which might be expected when the component is in normal use.


Coin Cell


We used a standard CR2032 watch battery. The readings for this sort of cell vary much more wildly than for an AA cell. We’d assumed this is due to internal heating of the cell, but in writing these notes we’ve started to wonder if it’s more about the chemistry that’s going on inside – if there’s a limit to the reaction rate, that would explain why the voltage drops away rapidly (particularly with high current drain cases), before the cell recovers after ‘resting.’ Comments welcome, and for now we’ll move on…

Taking photos of the meters is one way of dealing with rapidly-changing readings. Another approach would be to use analogue meters, which can be easier to read by eye.

At 6’09” you’ll see Christina using a ‘best fit’ ruler – a clear ruler with a slot through the middle. We recommend these! Our results:



With the increased uncertainty in the readings, Alom suggests repeating the whole experiment twice. Each repeat could be plotted onto the same axes and the gradients and y-intercepts compared. Students could then find the mean EMF and internal resistance, together with their associated uncertainties.

We would normally expect a 3 V cell to have an EMF of about 3 V, and an internal resistance which is much higher than the AA cell – which indeed is what we found, measuring an internal resistance of 15 Ω.

You might ask your students:

  • Is there a better way to record the fluctuating readings?
  • Is a simple mean a legitimate way to combine repeat readings?
  • What’s the best way to deal with data which looked bunched-up on a graph because you need to include the y-intercept? (You could investigate mathematical extrapolation methods here.)
  • Why do cells have different EMFs and internal resistance? What chemicals do they contain and how are they structured inside? (a useful resource here is Battery University, though it gets a little… detailed, shall we say?)

Other Notes

Costs

  • 50 AA cells should cost about £12.
  • 40 3 V coin cells should cost about £5.

Further Work

Some teachers like to challenge their students further by investigating the EMF and internal resistance of a cell made with copper and zinc electrodes and an item of fruit or a vegetable, for example: a ‘potato battery.’ Further guidance on this can be found at the Practical Physics website. Cutting the potato into different shapes can make for an interesting comparison.

Assessment

Common Practical Assessment Criteria

At the time of writing, the exam boards appear to agree that this practical might be used to address, in whole or in part:

  • CPAC 1: Follows written procedures
    • Correctly follows instructions to carry out the experimental techniques or procedures
  • CPAC 4: Makes and records observations.
    • Makes accurate observations relevant to the experimental or investigative procedure.
    • Obtains accurate, precise and sufficient data for experimental and investigative procedures and records this methodically using appropriate units and conventions. 

You can likely prioritise other CPACs should you so choose. There are some more notes on this in the draft student worksheet, below.

Student Worksheet

We’ve drafted a student worksheet for this practical, which you may find useful as a starting point:

Comments & Feedback

As ever, no single film can encompass everything one might wish to say about a practical. Please, leave comments with your thoughts about the approach we’ve taken, and your suggestions for alternatives or improvements.