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newSchoolWorks.com › VoTechWorks › Manufacturing & Marine › Industrial Maintenance › Industrial Electrical Systems for Manufacturing and Marine Maintenance › Lesson 2
MFG-INDU16-05 · Lesson 2 · 12.5 clock hours · theory

Electrical Fundamentals: Voltage, Current, Resistance, and Ohm's Law

Objective. The learner will apply Ohm's Law and Kirchhoff's Voltage and Current Laws to calculate unknown values in series, parallel, and series-parallel DC circuits, showing all work and achieving correct answers within 5% tolerance.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed engineer or certified journey-level 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.

Why Electrical Fundamentals Matter in Industrial and Marine Maintenance

Every motor starter, control panel, and shipboard distribution board obeys the same three relationships: voltage drives current through resistance, power is the product of voltage and current, and the total energy around any closed loop always balances. Master these relationships and you can predict, measure, and troubleshoot any DC circuit before you touch a wire.

Safety First

Before working on any electrical circuit, follow your facility's lockout/tagout (LOTO) procedure (29 CFR 1910.147 covers the general industry standard). Even on low-voltage bench circuits, treat every source as energized until you have personally verified it is de-energized with a tested meter. Wear safety glasses during bench work — resistors and leads can fail unexpectedly. Keep your free hand away from the circuit when probing with a live meter. Use a meter rated for the voltage present and inspect leads for cracked insulation before each use.

Voltage, Current, and Resistance

Voltage (E or V) is the electromotive force — the electrical pressure that pushes charge around a circuit. It is measured in volts (V) with a voltmeter connected in parallel across the component of interest.

Current (I) is the rate of flow of electric charge. It is measured in amperes (A) with an ammeter (or a DMM in current mode) connected in series so all current flows through it.

Resistance (R) is the opposition a material offers to current flow. It is measured in ohms (Ω). Always de-energize and isolate the component before measuring resistance; an energized circuit will damage the meter and give a false reading.

Ohm's Law

Georg Ohm established that voltage, current, and resistance are related by a single equation:

```

E = I × R

```

Rearranged for any unknown:

In a control-voltage divider supplying a 24 V relay coil, for example, you can calculate the dropping resistor value before installation — confirming the design is correct without guessing.

Watt's Law (Power)

Electrical power is the rate at which energy is converted. The basic form is:

```

P = I × E

```

Combined with Ohm's Law, two additional forms are useful:

Power is measured in watts (W). Knowing power lets you select correctly rated components — a resistor or indicator lamp must be rated above the actual power it dissipates or it will overheat and fail.

Series Circuits

In a series circuit, there is only one path for current. Key rules:

1. Current is the same through every component: I_total = I_1 = I_2 = …

2. Total resistance is the sum of all resistors: R_total = R_1 + R_2 + …

3. Voltage drops across each resistor and the drops add up to the source voltage (Kirchhoff's Voltage Law).

Parallel Circuits

In a parallel circuit, components share the same two nodes so voltage across each branch is equal. Key rules:

1. Voltage is the same across every branch: E_total = E_1 = E_2 = …

2. Total current is the sum of branch currents: I_total = I_1 + I_2 + … (Kirchhoff's Current Law)

3. Total resistance is found by: 1/R_total = 1/R_1 + 1/R_2 + …

Kirchhoff's Laws

Kirchhoff's Voltage Law (KVL): The algebraic sum of all voltages around any closed loop equals zero. In practice: the source voltage equals the sum of all voltage drops in that loop. This is why indicator lamps in a series string all dim when one resistance increases.

Kirchhoff's Current Law (KCL): The total current entering a junction equals the total current leaving it. This is why adding a parallel branch in a marine lighting circuit increases total current draw on the feeder — a critical calculation before adding loads to a panel.

Series-Parallel Circuits

Most industrial and marine circuits combine series and parallel sections. The strategy is to simplify: replace each parallel group with its equivalent resistance, then treat the result as a series circuit. Work systematically and label every step.

Reading Your DMM

For voltage: select DC volts, connect the red lead to the more-positive point, black lead to the more-negative point. For current: select the appropriate ampere range, break the circuit, and insert the meter in series. For resistance: de-energize the circuit, isolate the component, then connect the leads — polarity does not matter for resistance. Record all measured values with units in your lab notebook and calculate percent error:

```

% Error = |Measured − Calculated| ÷ Calculated × 100

```

A result within 5% confirms your calculations and your measurement technique are both sound.

Key terms9

Voltage (E)Electromotive force measured in volts (V); the electrical pressure that drives current through a circuit.
Current (I)The rate of flow of electric charge through a conductor, measured in amperes (A).
Resistance (R)The opposition a material presents to current flow, measured in ohms (Ω).
Ohm's LawThe relationship E = I × R, which states that voltage equals current multiplied by resistance in a DC circuit.
Watt's LawThe relationship P = I × E, which states that power in watts equals current in amperes multiplied by voltage in volts.
Kirchhoff's Voltage Law (KVL)The algebraic sum of all voltages around any closed loop in a circuit equals zero; source voltage equals the sum of all voltage drops.
Kirchhoff's Current Law (KCL)The total current entering any junction in a circuit equals the total current leaving that junction.
Series-Parallel CircuitA circuit that contains both series and parallel sections; solved by reducing parallel groups to equivalent resistances and then applying series-circuit rules.
Percent ErrorThe absolute difference between a measured value and a calculated value, divided by the calculated value and multiplied by 100; used to validate measurement accuracy.

Worked examples4

1. A control circuit has a 24 V DC source and a single resistor of 120 Ω. Find the current flowing and the power dissipated.
  1. Identify knowns: E = 24 V, R = 120 Ω.
  2. Apply Ohm's Law to find current: I = E ÷ R = 24 ÷ 120 = 0.2 A.
  3. Apply Watt's Law to find power: P = I × E = 0.2 × 24 = 4.8 W.
  4. State the result with units: I = 0.2 A (200 mA); P = 4.8 W.
Answer: I = 0.2 A; P = 4.8 W
2. Three resistors — R1 = 100 Ω, R2 = 150 Ω, R3 = 250 Ω — are connected in series across a 24 V DC supply. Find the total resistance, circuit current, and voltage drop across each resistor.
  1. Find total resistance: R_total = R1 + R2 + R3 = 100 + 150 + 250 = 500 Ω.
  2. Find circuit current using Ohm's Law: I = E ÷ R_total = 24 ÷ 500 = 0.048 A (48 mA). Current is the same through every resistor in a series circuit.
  3. Find voltage drop across R1: E1 = I × R1 = 0.048 × 100 = 4.8 V.
  4. Find voltage drop across R2: E2 = I × R2 = 0.048 × 150 = 7.2 V.
  5. Find voltage drop across R3: E3 = I × R3 = 0.048 × 250 = 12.0 V.
  6. Verify with KVL: E1 + E2 + E3 = 4.8 + 7.2 + 12.0 = 24.0 V ✓
Answer: R_total = 500 Ω; I = 0.048 A; E1 = 4.8 V; E2 = 7.2 V; E3 = 12.0 V
3. Two resistors — R1 = 200 Ω and R2 = 300 Ω — are connected in parallel across a 12 V DC supply. Find the total resistance, each branch current, and total current.
  1. Find total resistance using the reciprocal formula: 1/R_total = 1/200 + 1/300 = 3/600 + 2/600 = 5/600, so R_total = 600 ÷ 5 = 120 Ω.
  2. Voltage across each branch equals source voltage (parallel rule): E1 = E2 = 12 V.
  3. Find branch current through R1: I1 = E ÷ R1 = 12 ÷ 200 = 0.06 A (60 mA).
  4. Find branch current through R2: I2 = E ÷ R2 = 12 ÷ 300 = 0.04 A (40 mA).
  5. Apply KCL to find total current: I_total = I1 + I2 = 0.06 + 0.04 = 0.10 A (100 mA).
  6. Verify with Ohm's Law: I_total = E ÷ R_total = 12 ÷ 120 = 0.10 A ✓
Answer: R_total = 120 Ω; I1 = 60 mA; I2 = 40 mA; I_total = 100 mA
4. A series-parallel circuit has a 24 V DC source. R1 = 80 Ω is in series with a parallel combination of R2 = 120 Ω and R3 = 120 Ω. Find the total resistance, total current, voltage drop across R1, and voltage across the parallel section.
  1. Find the equivalent resistance of the parallel section (R2 ∥ R3): 1/R_parallel = 1/120 + 1/120 = 2/120, so R_parallel = 60 Ω.
  2. Find total circuit resistance: R_total = R1 + R_parallel = 80 + 60 = 140 Ω.
  3. Find total current: I_total = E ÷ R_total = 24 ÷ 140 ≈ 0.1714 A (171.4 mA).
  4. Find voltage drop across R1: E_R1 = I_total × R1 = 0.1714 × 80 ≈ 13.71 V.
  5. Find voltage across the parallel section using KVL: E_parallel = 24 − 13.71 ≈ 10.29 V.
  6. Verify with Ohm's Law: E_parallel = I_total × R_parallel = 0.1714 × 60 ≈ 10.29 V ✓
Answer: R_total = 140 Ω; I_total ≈ 171.4 mA; E_R1 ≈ 13.71 V; E_parallel ≈ 10.29 V

The math in this lesson2

Learners compute total resistance of series, parallel and series-parallel resistor networks.
A-SSE.1A-CED.4
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor-led derivation of Ohm's Law (E = IR), Watt's Law (P = IE), and both Kirchhoff's laws using industrial examples such as control-voltage dividers and indicator lamp circuits; learners complete a guided worksheet with 15 calculation problems. · Learners build three DC bench circuits (series, parallel, series-parallel) using a variable DC power supply and fixed resistors, measure voltage drops and branch currents with a DMM, then compare measured values to calculated predictions and record percentage of error in their lab notebook. · Peer-teaching activity: each learner is assigned one circuit type and must explain the current path and voltage distribution to a partner using the physical circuit and a whiteboard sketch before the instructor checks understanding.
Materials: Variable DC power supply (0–30 V), fixed resistors (assorted), digital multimeters, breadboards, connecting leads, NCCER Industrial Maintenance Electrical Level One module, scientific calculators, graph paper for circuit sketches
Check: Ten-problem calculation quiz plus measurement accuracy check: learner's DMM readings must match calculated values within 5%; passing score 80% on quiz and all measurements within tolerance.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NCCER Industrial Maintenance — Electrical Level One: DC circuits
1. A resistor in a DC control circuit measures 470 Ω. The voltage across it is 9.4 V. What is the current through the resistor?
MSSC CPT — Safety and Quality; electrical principles
2. In a series DC circuit with three resistors, which statement about current is correct?
NCCER Industrial Maintenance — Electrical Level One: DC circuits
3. A parallel circuit has two branches: one draws 0.5 A and the other draws 0.3 A. What does Kirchhoff's Current Law tell you about the total current supplied by the source?
NCCER Industrial Maintenance — Electrical Level One: DC circuits
4. Two resistors of 60 Ω each are connected in parallel. What is their combined equivalent resistance?
MSSC CPT — Manufacturing Processes and Production; electrical power
5. A 12 V battery powers an indicator lamp that draws 0.25 A. What is the power dissipated by the lamp?
NCCER Industrial Maintenance — Safety and Tools; MSSC CPT Safety
6. A technician uses a DMM to measure resistance in a circuit and gets an unexpectedly high reading. Which action should be taken first before trusting the result?
NCCER Industrial Maintenance — Electrical Level One: DC circuits
7. In a series circuit, three resistors have voltage drops of 5 V, 9 V, and 7 V. What does Kirchhoff's Voltage Law state about the source voltage?
NCCER Industrial Maintenance — Electrical Level One: DC circuits
8. A series-parallel circuit has a 48 V source. A 40 Ω resistor is in series with a parallel combination whose equivalent resistance is 20 Ω. What is the voltage across the parallel section?
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