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

Why Ohm's Law Matters for the NAPT

Electricity questions make up a substantial share of the NAPT physics content, and for good reason: every rating in the Nuclear Field program works with electrical systems, from an Electrician's Mate maintaining switchboards to a Machinist's Mate troubleshooting motor-driven equipment. Ohm's Law is the single most important relationship in basic electricity — it connects voltage, current, and resistance, and it is the starting point for analyzing any circuit, simple or complex.

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 same relationship also gives I = V/R and R = V/I — memorize all three forms, because NAPT questions can ask you to solve for any of the variables.

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.

Real shipboard electrical distribution is built almost entirely on parallel wiring for exactly this last reason — one failed light fixture or motor should not take down every other device on the same circuit.

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.