Physics IA · B · The particulate nature of matter · topic 11 of 30

Solar cell: does output follow the cosine of the angle? · IB Physics IA idea: guide, sample graph and step-by-step plan

everyday physics, careful control needed

Tilt a solar panel and the power drops. The textbook says by a factor of cos θ. Check it, and find out where it stops being true.

Difficulty●●○ Medium
KitStandard: small solar cell, lamp, ammeter or voltmeter
TimeAbout 10 hours
FitsSL and HL
  • ✓ you like energy and renewables
  • ✓ you can build a rotating mount with a clear angle scale
  • ✓ you enjoy a model that is almost right

The big idea

← is it really just cos θ?

The power a surface receives from a distant source is proportional to the cosine of the angle between the light and the surface's normal, because the same beam is spread over a bigger area. A cell's short-circuit current should follow that cosine, but its voltage hardly changes. Real cells also reflect more light at large angles. Test cos θ, and decide what the deviations are telling you. The big skill is controlling the light so that only the angle changes.

Make it yours: pick one twist

Copying a classic won't show your choices. Pick one of these (or invent your own) and your IA becomes yours.

Swipe for more twists →

Current versus voltage

Measure both the short-circuit current and the open-circuit voltage at each angle.

→ You can show that one follows the cosine and the other barely moves, and explain why from how a cell works.
Power into a load

Connect a fixed resistor and measure the power at each angle.

→ Closer to real use, but the answer depends on the load, so choose and justify it.
Compare cells or covers

Two cell types, or the same cell with and without a clear cover.

→ Tests whether the deviation at large angles depends on reflection at the surface.
Change the distance too

Repeat the angle series at two distances from the lamp.

→ Checks the inverse-square effect and keeps it separate from the angle effect.
Use sunlight

Record outdoors across a day with a fixed tilt.

→ The angle changes with time but so does the intensity; a messy, real-world version that needs a light sensor beside the cell.
Add a light sensor

Use a light sensor as a reference at each angle.

→ Separates changes in the light from changes in the cell; improves your evaluation of the lamp's stability.

Your Physics IA research question: run the check

write it FIRST, then check it

Write your own question first. Then make sure it ticks every box:

  • Names one independent variable with its range (which angles, in degrees, measured from the normal or the surface?).
  • Names the dependent variable and how you measure it (short-circuit current, open-circuit voltage or power into a load).
  • Says what stays fixed: the lamp, the distance, the cell, the background light and the warm-up time.
  • Says what you will compare with (cos θ, or another model for the angle dependence).
  • Is narrow enough for about 10 hours, with at least 7 angles and repeats.

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The set-up

A lamp at a fixed distance, a cell on a pivot with an angle scale, and everything else dark. Draw your own version with your real distances.

θAlamp: fixed distance,warm it up firstcell pivots about its own face:read θ from the angle scaleammeter: short-circuit currentcover everything butthe lamp: stray light

How your Physics IA could be laid out

The usual order for a topic like this, what each part needs to show, and roughly how much of your 3,000 words it takes. The words are all yours.

Research question and context~250
Your question, where panel angle matters (rooftop panels, solar-powered calculators, satellites) and what you expect for the graph.
Background physics~450
Intensity and the cosine of the angle, how a solar cell makes current and voltage, and what changes at large angles.
Variablestable
Independent, dependent and controlled variables with how each is set and kept constant.
Method~400
How you mount and rotate the cell, define zero angle, block stray light, wait for the lamp to settle, and read the meter.
Safety, ethics, environment~60
A hot lamp, not looking into a bright lamp, mains electrical safety.
Raw datatable
Angle and meter readings with units, resolution and a dark reading.
Processing~250
Subtracting the dark reading, uncertainty in angle and in current, one worked example for each type of calculation.
Graphs and analysis~400
Output against angle with the cosine curve, and a second graph against cos θ; what the gradient and deviations mean.
Conclusion~400
How closely cos θ describes your data, over what range, and what the deviations are.
Evaluation~650, the biggest part!
Weaknesses ranked by effect on your result, linked to specific improvements.
Referencesnot counted
Sources for the theory and the cell.

What your Physics IA graph could look like

dark reading first ✓

Made-up data, to show the form of a strong graph, not the answer. Yours will look different. example only

010203040506070800102030405060Angle from the normal θ / ° (± 2°)Short-circuit current I / mA (± 0.8 mA, from repeats)I ∝ cos θstraight line in θ (a common guess)your data, with error barsdata fall below cos θ at largeangles: what could cause that?ILLUSTRATIVE · MADE-UP DATA
  • Plot against the angle from the normal. If you measured from the surface, say so, and convert.
  • Error bars: an angle error matters most where the curve is steepest, so look at the middle angles.
  • The cosine and the straight line are both drawn so the reader can see why one is better.
  • Subtract the reading in the dark first, otherwise stray light adds a constant and bends the curve.
  • Another graph to consider: I against cos θ. If the cosine law holds, that is a straight line through the origin, and its curvature at the end is easy to see.

Which uncertainty matters most?

Rank by the effect on your result, here the current at 60°. The steeper the curve, the more a small angle error costs you.

Angle reading (±2° at 60°)6%Lamp drift (assumed ±3%)3%Stray light (about 0.5 mA)2.2%Meter (±0.1 mA)0.4%biggest effect: discuss this first!% uncertainty in I at θ = 60°ILLUSTRATIVE · MADE-UP NUMBERS

Your game plan

go up AND down in angle to spot drift

Tick steps off as you go. We'll remember on this device.

0 of 10 done

  1. Read and predictFind out why intensity falls as cos θ and how a solar cell produces current and voltage. Predict the shape of both graphs, and what you expect at large angles.
  2. Trial run (1 lesson)Set up the lamp and cell, take readings at five angles, then again after ten minutes. Does the lamp drift? Does stray light matter? Is the zero angle easy to find?
  3. Control the lightChoose a distance, a warm-up time and a way to block stray light. Take a dark reading.
  4. Choose range and repeatsChoose at least 7 angles from near 0° to a large angle, and how many repeats. Write down your reasons.
  5. Collect the dataGo up and down in angle to test for drift. Record raw readings with units and resolution.
  6. ProcessSubtract the dark reading, find uncertainties in angle and current, and decide how to show them.
  7. Graph and fitPlot output against angle with the cosine curve, then against cos θ. Add error bars.
  8. Compare with theoryWhere does the data follow cos θ and where does it stop? What explanation fits the deviation?
  9. EvaluateRank the uncertainties and systematic errors by effect on your conclusion and link every improvement to a specific weakness.
  10. Check before your teacher's draftRun the checklist above, then get your RQ or draft checked. Your teacher reads one draft only.

Physics you'll need

Traps to avoid in this Physics IA

  • Stray light from windows, screens or a second lamp, adding an unknown constant.
  • Measuring angle from the surface but using a cos θ model that assumes the normal.
  • A lamp that is still warming up, so the output drifts through your run.
  • Letting the distance from lamp to cell change as the cell turns.
  • Only reading at a few small angles, where cos θ barely changes.
  • Measuring voltage and calling it "output" without saying why it barely changes.

More Physics IA ideas like this

Make sure it's yours

This guide shows how a topic like this is usually approached. It is not an IA. Your question, choices, data, analysis and words must be your own: change something, tell your teacher where the idea came from, and follow your school's rules on outside help.

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