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Solar Exam Math I: Ohm's Law, Power, Temperature Correction & String Sizing

Solar Exam Math I: Ohm's Law, Power, Temperature Correction & String Sizing

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Here's one that matters more than its name lets on — Solar Exam Math I. If you remember one thing, make it this: almost every NABCEP calculation comes back to a handful of formulas — Ohm's law, the power formula, series-and-parallel rules, and temperature correction — and if you can do them by hand without thinking, you'll have time left for the hard questions. Let's work them.

Educational content only — not official NABCEP material, electrical design, or a substitute for a licensed electrician. Eligibility rules, exam content, fees, and renewal requirements are set by NABCEP and change; always confirm them in NABCEP's current candidate handbook and exam blueprint. Real installations must follow the NEC (NFPA 70) edition adopted by your Authority Having Jurisdiction, the manufacturers' instructions, and your utility's rules.

Ohm's law and the power formula

Example 1. A 400 W module has Vmp = 37.0 V. What is Imp? I = P / V = 400 / 37.0 = 10.8 A

Example 2. A conductor has 0.25 ohm of total resistance and carries 12 A. Voltage lost? Power lost? V = 12 x 0.25 = 3.0 V. P = 12² x 0.25 = 36 W.

Watch the trap: power (W, kW) is a rate; energy (Wh, kWh) is power over time. A 5 kW array running at full output for 4 hours makes 20 kWh.

Series and parallel

Example 3. 12 modules in series, each Vmp = 40 V, Imp = 10 A. String Vmp = 12 x 40 = 480 V; current = 10 A; power = 480 x 10 = 4,800 W.

Example 4. Two of those strings in parallel: 480 V, 20 A, 9,600 W.

For Voc and Isc the same rules apply: series adds Voc; parallel adds Isc.

Temperature correction

Module voltage rises in the cold and falls in the heat. The datasheet gives a temperature coefficient in either %/°C or V/°C, relative to 25°C (standard test conditions).

Percent form: Corrected value = STC value x [1 + (T - 25) x coefficient] Volt form: Corrected Voc = Voc + (T - 25) x coefficient (in V/°C)

Example 5 (percent). Voc = 45.0 V, coefficient = -0.28%/°C, design low = -20°C. (T - 25) = -45; -45 x -0.0028 = +0.126; 45.0 x 1.126 = 50.7 V

Example 6 (volts). Voc = 45.0 V, coefficient = -0.13 V/°C, design low = -20°C. -45 x -0.13 = +5.85; 45.0 + 5.85 = 50.9 V

Example 7 (power in the heat). A 400 W module at a 65°C cell temperature, Pmax coefficient = -0.35%/°C. (65 - 25) = 40; 40 x -0.0035 = -0.14; 400 x 0.86 = 344 W

Know the signs: cold (below 25°C) gives a negative (T - 25); a negative coefficient times a negative number is positive, so voltage goes up. Hot gives a positive (T - 25), and voltage or power goes down.

If no coefficient is given, the exam may expect the NEC Table 690.7(A) correction factor — find the row for the temperature and multiply.

String sizing

Maximum modules per string = maximum allowed voltage / cold-corrected Voc → round down. Minimum modules per string = inverter minimum MPPT (or start-up) voltage / hot-corrected Vmp → round up.

Example 8. Inverter max DC input 600 V. Cold-corrected Voc from Example 5 = 50.7 V. 600 / 50.7 = 11.8 → 11 modules (11 x 50.7 = 558 V).

Example 9. Inverter MPPT minimum 240 V. Module Vmp = 37.0 V, Vmp coefficient -0.35%/°C, hot cell temperature 70°C. (70 - 25) = 45; 45 x -0.0035 = -0.1575; 37.0 x 0.8425 = 31.2 V. 240 / 31.2 = 7.7 → round up to 8 modules. (Had the minimum been 250 V, 250 / 31.2 = 8.01 would force 9 — never round a minimum down.)

Remember the voltage ceilings in 690.7: 600 V on one- and two-family dwellings, 1,000 V on other buildings, and up to 1,500 V for systems not on buildings — plus the inverter's and module's own maximum system voltage. The lowest limit governs.

Going Deeper (Intermediate)

Circuit current math also shows up: 690.8 maximum current for a PV source circuit = Isc x 1.25, and conductor/OCPD sizing = that value x 1.25 (overall Isc x 1.56). Inverter output circuit OCPD = inverter continuous output current x 1.25, rounded up to a standard breaker size.

Example 10. Isc = 11.2 A. Max current = 14.0 A. Minimum conductor/OCPD basis = 17.5 A → 20 A fuse (if a fuse is required and the module's series fuse rating allows).

Advanced / Pro-Level

On the exam, write the formula first, then plug in numbers, with units at every step. It catches mistakes like using Vmp where Voc belongs, or a percent coefficient as if it were volts. Check reasonableness: a cold-corrected Voc should be roughly 10–15% above STC in most U.S. climates; a result 50% higher means a decimal error. Learn your calculator's memory functions so you don't re-key long numbers.

Practice Challenge

Modules: Voc 41.5 V, Vmp 34.8 V, Voc coefficient -0.27%/°C, Vmp coefficient -0.36%/°C. Site: design low -25°C, hot cell 72°C. Inverter: 600 V max, 200 V MPPT minimum. Find the string-size window. (Answer: cold Voc = 41.5 x [1 + (-50)(-0.0027)] = 41.5 x 1.135 = 47.1 V → 600 / 47.1 = 12.7 → max 12. Hot Vmp = 34.8 x [1 + (47)(-0.0036)] = 34.8 x 0.8308 = 28.9 V → 200 / 28.9 = 6.9 → min 7. Window: 7 to 12 modules.)

In Practice

Make a one-page formula sheet in your own handwriting and redo it from memory each week until you can write it cold. Then check every practice problem against it.

Common Mistakes to Avoid

Takeaway: Ohm's law, the power formula, series-parallel rules, and temperature correction are the backbone of exam math — write the formula, carry the units, watch the signs, round string sizes the safe way, and check that every answer makes sense.

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