Lab 101-B — A Solar Cell as a Light Sensor: Angle and Intensity
Goes with: Units 9 and 10. Time: 2–3 hours on a clear day. Cost: about \(40–\)80 (estimate).
Goal
Measure a real silicon cell's short-circuit current (\(I_{sc}\)) as you (1) rotate it away from the Sun and (2) attenuate the light with layers of window screen, and (3) compare sunlight with a lamp. Test the cosine law and the linearity of \(I_{sc}\) with irradiance; see reflection losses at steep angles.
What you will learn
- \(I_{sc} \propto\) irradiance (photon flux).
- The cosine law, and deviations at large angles from Fresnel reflection.
- How to log data properly (the habit employers want).
Shopping list
| Item | Spec / example | Qty | Approx. cost (estimate) | Where |
|---|---|---|---|---|
| Small mono-Si cell or mini panel | bare mono cell 0.5 V, 100–500 mA (e.g., 52 × 19 mm to 125 × 125 mm pieces) and/or an encapsulated 5–6 V 1–2 W mini panel | 2–4 | $5–15 each | Adafruit, SparkFun, Amazon, eBay |
| Digital multimeter | must have a 10 A DC current range; e.g., Klein Tools MM400 class or Fluke 115 class | 1 | $25–40 (Klein) / $150+ (Fluke) | Amazon, Home Depot |
| Test leads with alligator clips | — | 1 set | $8 | Amazon |
| Protractor (large) + cardboard/plywood stand | 15–30 cm protractor; a hinged board works | 1 | $5–10 | office/hardware store |
| Window screen (fibreglass) | ~0.5 m² roll offcut | 1 | $5–10 | hardware store |
| Thermometer | IR thermometer or K-type probe (to note cell temperature) | 1 | $15–25 | Amazon |
| Optional lux meter | e.g., Dr.Meter LX1330B class | 1 | $20–30 | Amazon |
| Optional lamp | 12 V halogen or 50 W-equivalent LED flood | 1 | $10–20 | hardware store |
Safety
- Sun/UV exposure: hat, sunscreen, sunglasses. Never look at the Sun.
- Keep meter leads in the correct jacks: the 10 A jack for current, back to V/Ω afterwards (a meter left on 10 A and put across a battery is a short circuit).
- Small cells give < 1 A and ≤ 6 V — electrically safe. Bare cells are fragile and sharp when broken: handle by edges; dispose shards in a sharps container.
Why "short-circuit current with a multimeter" works
A multimeter's current range has a tiny internal resistance (a shunt of ~0.01–0.1 Ω on the 10 A range), so connecting it directly across the cell is nearly a short circuit: you read \(I_{sc}\). Use the 10 A range for cells that might exceed 200 mA.
Setup
- Mount the cell flat on a board hinged to a base so you can tilt it; fix the protractor at the hinge with a pointer (straw or wire) along the board's normal.
- Point the base so that at 0° the cell faces the Sun directly (its shadow of a toothpick stuck perpendicular to the board vanishes — the "shadow-stick" alignment trick).
- Connect the meter: red lead to 10 A jack, black to COM, clips to cell + and −.
Procedure
Part 1 — Angle. Record \(I_{sc}\) at 0°, 10°, 20° … 80°, and 85°. Return to 0° every few readings to check the Sun hasn't changed (clouds!). Note time and cell temperature.
Part 2 — Intensity. At 0°, cover the cell with 0, 1, 2, 3, 4, 5 layers of window screen (lay them flat, same orientation). Record \(I_{sc}\). Measure the transmission of one layer as \(T_1 = I_{sc}(1)/I_{sc}(0)\).
Part 3 — Lamp vs Sun. Indoors, place the cell under the lamp at a distance giving the same \(I_{sc}\) as sunlight at 0°, if possible. Measure the lux reading at both (optional), and the cell's temperature after 5 min under each.
Part 4 (optional) — Open-circuit voltage. Switch to DC volts and record \(V_{oc}\) for each screen layer count.
Log everything to a CSV: timestamp, part, angle_deg, layers, Isc_A, Voc_V, cell_T_C, sky_notes.
Analysis
- Plot \(I_{sc}(\theta)/I_{sc}(0)\) against θ together with \(\cos\theta\) and with \(\cos\theta \times (1-R(\theta))/(1-R(0))\) using \(R\) for glass (encapsulated panel) or bare Si (bare cell) from Unit 9.
- Plot \(\ln I_{sc}\) against number of layers: a straight line means each layer transmits the same fraction (Beer–Lambert-like behaviour), confirming that \(I_{sc}\) is proportional to irradiance.
- Plot \(V_{oc}\) against \(\ln I_{sc}\): the slope should be about \(n k_BT/q\) per series-connected cell (≈ 26 mV × n for a single cell; multiply by cell count for a mini panel).
Expected results
- Up to ~50°, measured \(I_{sc}\) follows \(\cos\theta\) within a few per cent. Beyond ~60° it falls below the cosine curve — reflection loss (more obvious for encapsulated panels with flat glass). At 80° expect roughly 10 % of the 0° reading rather than 17 %.
- Diffuse skylight puts a floor under the reading at large angles (the cell still sees sky), so measurements at 85° may exceed the pure-beam prediction.
- Each screen layer typically transmits ~60–75 % (estimate; depends on mesh); \(\ln I_{sc}\) vs layers is linear.
- \(V_{oc}\) changes only tens of millivolts per cell while \(I_{sc}\) drops several-fold.
- Under a halogen lamp matched for \(I_{sc}\), the lux reading will be much lower than in sunlight and the cell gets hotter — the lamp supplies lots of IR photons that the cell uses (up to 1107 nm) or absorbs as heat, but the eye-weighted lux meter ignores.
How to interpret
Current tracks photon flux — this is why reference cells (calibrated silicon cells) are used to set flash-tester irradiance. Angular losses beyond the cosine factor are what AR coatings and textured glass reduce. The lamp comparison shows why "same brightness to the eye" is not "same light to a solar cell".
Sources
- PVEducation: "Short-Circuit Current", "Effect of Light Intensity".
- Fresnel equations (Unit 9).