DC Circuit Theory: Voltage, Current, Resistance, and Power
Objective. Given a DC circuit description, the student will correctly apply Ohm's Law and Watt's Law to calculate voltage, current, resistance, and power with 100% accuracy on a 10-problem set.
This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.
VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.
DC Circuit Theory: Voltage, Current, Resistance, and Power
Every photovoltaic system is, at its core, a DC electrical circuit. Before you can safely size conductors, select overcurrent protection, or troubleshoot a string that is underperforming, you must be able to calculate voltage, current, resistance, and power with confidence. This lesson covers the two laws you will use on every job: Ohm's Law and Watt's Law.
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The Four Fundamental Quantities
Voltage (V) is electrical pressure — the force that pushes electrons through a conductor. It is measured in volts (V). On a PV module spec sheet you will see two voltage ratings: open-circuit voltage (Voc) and maximum-power-point voltage (Vmp).
Current (I) is the flow rate of electrons through a conductor. It is measured in amperes, or amps (A). The spec sheet lists short-circuit current (Isc) and maximum-power-point current (Imp).
Resistance (R) opposes the flow of current. It is measured in ohms (Ω). Every conductor, connection, and component adds some resistance to the circuit.
Power (P) is the rate at which electrical energy is converted to another form (heat, light, mechanical work, or stored energy). It is measured in watts (W) or kilowatts (kW).
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Ohm's Law
Ohm's Law states that in a DC resistive circuit, voltage equals current multiplied by resistance:
> V = I × R
Rearranged to solve for the other quantities:
- I = V ÷ R (current equals voltage divided by resistance)
- R = V ÷ I (resistance equals voltage divided by current)
A useful memory tool is the Ohm's Law triangle: write V at the top, I and R at the bottom. Cover the quantity you want to find and the remaining symbols show the calculation.
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Watt's Law
Watt's Law relates power to voltage and current:
> P = V × I
Combined with Ohm's Law, two additional forms are commonly used:
- P = I² × R (useful when you know current and resistance)
- P = V² ÷ R (useful when you know voltage and resistance)
Rearranged:
- V = P ÷ I
- I = P ÷ V
On a 300 W module operating at its maximum power point, if Vmp = 32.5 V, then Imp = 300 ÷ 32.5 ≈ 9.23 A. You will use this relationship constantly when verifying spec-sheet values.
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Applying These Laws to PV Circuits
Series Strings
When modules are wired in series, voltages add and current stays the same throughout the string. If four 300 W modules each have a Vmp of 32.5 V and an Imp of 9.23 A:
- String Vmp = 32.5 × 4 = 130 V
- String Imp = 9.23 A (unchanged)
- String power = 130 × 9.23 ≈ 1,200 W
Parallel Arrays
When strings are wired in parallel, currents add and voltage stays the same. Two of the above strings in parallel:
- Array Vmp = 130 V (unchanged)
- Array Imp = 9.23 × 2 = 18.46 A
- Array power = 130 × 18.46 ≈ 2,400 W
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Units and Decimal Precision
Always write the unit with every number. A naked "32.5" means nothing on an inspection document; "32.5 V" is unambiguous. Round calculated answers to two decimal places unless a spec sheet or problem states otherwise. Carry full precision through intermediate steps to avoid rounding error.
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Safety Notes
PV modules generate voltage the moment light hits them — you cannot switch off the sun. Even a single 300 W module can produce lethal DC voltage and arc-flash energy in full sunlight.
- Lockout/tagout (LOTO): Follow your site's written LOTO procedure before working on any part of the circuit. Cover modules with an opaque tarp when you must de-energize the DC side.
- PPE: Wear voltage-rated insulated gloves appropriate for the system voltage, safety glasses, and arc-flash-rated clothing when the hazard assessment requires it.
- Never assume a circuit is de-energized. Use a calibrated meter to verify voltage is absent before touching conductors.
- DC arc flash: DC arcs are harder to extinguish than AC arcs. Treat every DC conductor as energized until proven otherwise.
Understanding Ohm's Law and Watt's Law helps you recognize when a measured value is dangerously outside the expected range — an essential troubleshooting and safety skill.
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Summary
| Law | Primary Formula | Common Rearrangements |
|---|---|---|
| Ohm's Law | V = I × R | I = V ÷ R; R = V ÷ I |
| Watt's Law | P = V × I | V = P ÷ I; I = P ÷ V; P = I² × R |
Master these two laws and you have the mathematical foundation for every electrical calculation in this program.
Key terms10
Worked examples4
- Identify the known values: V = 32.5 V, I = 9.23 A.
- Select the correct formula: P = V × I.
- Substitute: P = 32.5 V × 9.23 A.
- Calculate: P = 299.975 W, rounded to 300.00 W.
- Identify the known values: I = 18.46 A, R = 0.75 Ω.
- Select the correct formula: V = I × R.
- Substitute: V = 18.46 A × 0.75 Ω.
- Calculate: V = 13.845 V, rounded to 13.85 V.
- Identify the known values: P = 3,200 W, V = 320 V.
- Select the correct formula: I = P ÷ V.
- Substitute: I = 3,200 W ÷ 320 V.
- Calculate: I = 10.00 A.
- For a series string, voltages add and current is unchanged: String Vmp = 32.5 V × 4 = 130.00 V.
- String Imp = 9.23 A (current is the same throughout a series string).
- Calculate string power: P = V × I = 130.00 V × 9.23 A = 1,199.90 W, rounded to 1,199.90 W (≈ 1,200 W).
- Verify with nameplate: 4 modules × 300 W = 1,200 W — results are consistent.
The math in this lesson2
- MA7 1 · Expressions and Equations — Variables and expressions A-SSE.1
- MA7 2 · Expressions and Equations — Order of operations A-SSE.1
- MA7 5 · Expressions and Equations — Literal equations A-CED.4
- BZ5 3 · Money at Work — Markup versus margin A-CED.4
- BZ5 9 · Interest, Credit and Saving — Simple interest A-SSE.1
- BZ5 21 · The Small Business Ledger — The income statement A-SSE.1
Materials: Whiteboard, sample PV module spec sheets (e.g., 300 W module with Voc, Isc, Vmp, Imp listed), scientific calculators, student workbook Chapter 1, Dunlop 'Photovoltaic Systems' textbook (NJATC).
Check: 10-question written quiz covering Ohm's Law and Watt's Law applied to DC PV circuits; pass mark 80% (8/10 correct); instructor reviews each incorrect answer with the student before moving on.
Practice check8
Answer each question, then check it. Nothing is recorded; this is your own practice.
