4.2 Electricity: Ohm's Law & Series/Parallel Circuits

Editorial Scope

Ohm's law and simple series/parallel circuits are standard introductory electricity topics. They appear here as transferable STEM review, not because the Navy has published them as NAPT content or tied them to a particular rating task.

The Three Core Quantities

• Voltage (V), measured in volts, is the electrical potential difference that pushes current through a circuit — think of it as the electrical push that drives charge from one point to another.
• Current (I), measured in amperes (amps, A), is the rate of flow of electric charge through a circuit.
• Resistance (R), measured in ohms (Ω), is a material's opposition to the flow of current.

Ohm's Law ties these together: V = IR. Rearranged algebraically, this relationship also gives I = V/R and R = V/I; all three forms are useful in the local circuit exercises.

Worked Example: A 12V battery is connected to a 4Ω resistor. What current flows through the circuit?

I = V/R = 12 V ÷ 4 Ω = 3 A

Power in Electrical Circuits

Electrical power (P), measured in watts (W), is the rate at which a circuit converts electrical energy into another form (heat, light, motion). Three equivalent formulas calculate it, and all three must give the same answer for the same circuit:

P = VI = I²R = V²/R

Worked Example: Using the circuit above (12V, 3A, 4Ω), find the power dissipated.

P = VI = 12 V × 3 A = 36 W Check with P = I²R = (3 A)² × 4 Ω = 9 × 4 = 36 W ✓

Both formulas agree: the resistor dissipates 36 W.

Series Circuits

A series circuit connects components end-to-end along a single path, so current has only one route to follow. Three rules define series behavior:

1. Current is identical at every point in the circuit: I_total = I1 = I2 = I3…
2. Total resistance is the sum of all individual resistances: R_total = R1 + R2 + R3…
3. Voltage divides across each resistor in proportion to its resistance, and the individual voltage drops always add up to the source voltage.

Worked Example: A 20V battery is connected in series with two resistors, R1 = 6Ω and R2 = 4Ω. Find the total resistance, the current, and the voltage drop across each resistor.

R_total = R1 + R2 = 6 + 4 = 10 Ω I = V/R_total = 20 V ÷ 10 Ω = 2 A V1 = I × R1 = 2 A × 6 Ω = 12 V V2 = I × R2 = 2 A × 4 Ω = 8 V

Check: V1 + V2 = 12 + 8 = 20 V, matching the source voltage exactly. This check — that the voltage drops always sum to the source voltage — is a preview of Kirchhoff's Voltage Law, covered in the next section.

Parallel Circuits

A parallel circuit connects components across the same two nodes, giving current multiple paths to follow. Parallel rules are essentially the mirror image of series rules:

1. Voltage is identical across every branch, and equal to the source voltage.
2. Total current is the sum of the currents in each branch: I_total = I1 + I2 + I3…
3. Total resistance is found from the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3… — and total resistance is always smaller than the smallest individual resistor.

Worked Example: A 12V source is connected to two resistors in parallel, R1 = 6Ω and R2 = 3Ω. Find the total resistance and the current through each branch.

1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so R_total = 2 Ω I_total = V/R_total = 12 V ÷ 2 Ω = 6 A I1 = V/R1 = 12 V ÷ 6 Ω = 2 A I2 = V/R2 = 12 V ÷ 3 Ω = 4 A

Check: I1 + I2 = 2 + 4 = 6 A, matching the total current calculated directly.

Parallel wiring also illustrates why opening one branch need not interrupt every other branch.

Continue to section 4.3, where Kirchhoff's Laws generalize these same series and parallel rules to circuits with multiple loops and junctions that cannot be solved with series/parallel reduction alone.