TL;DR — Ohm's law (E = I × R) and the power formulas (P = EI, P = I²R, P = E²/R) drive nearly every DC circuit calculation on the exam; know how series circuits divide voltage, how parallel circuits divide current, and how cell chemistry — not cell size — fixes terminal voltage.
What the Rule Says
Cells and Batteries
A battery converts chemical energy directly into electrical energy. The fundamental unit is the cell: two dissimilar electrodes (positive and negative plates) immersed in an electrolyte. Chemical action frees electrons at the negative plate and removes them at the positive, establishing a potential difference; connecting a load closes the circuit and allows current to flow. NEETS Mod. 1 §2-1
Primary cells (carbon-zinc, alkaline) are not rechargeable — the electrode material is consumed and the cell is discarded when exhausted. Secondary (storage) cells (lead-acid, nickel-cadmium) are reversible: forcing current backward through the cell restores the plates and electrolyte, allowing repeated recharge cycles.
Cell voltage is set by electrode/electrolyte chemistry, not by physical size. A lead-acid cell is nominally 2.1 V; a nickel-cadmium cell is approximately 1.2 V regardless of how large the cell is. Physical size determines amp-hour capacity (how long the cell can sustain a given current), not voltage. A "battery" is technically two or more cells connected together.
Every cell has internal resistance. Under load, terminal voltage equals the open-circuit EMF minus the internal-resistance voltage drop (I × r_internal). A cell with high internal resistance may show a normal no-load voltage yet deliver very little usable current — a critical troubleshooting point for emergency battery banks.
Ohm's Law and Power
Ohm's law: E = I × R, rearranged as I = E/R and R = E/I. Given any two of the three quantities, the third is determined. NEETS Mod. 1 §3-1
Resistance depends on four factors: material resistivity, conductor length (longer = higher resistance), cross-sectional area (larger = lower resistance), and temperature (for metals, resistance increases with temperature).
Electrical power in watts: P = E × I. Substituting Ohm's law gives the two derived forms: P = I²R and P = E²/R. The I²R form is the most important for practical work — heat dissipated in a resistance rises with the square of the current, which is why undersized conductors and high-resistance connections overheat disproportionately. Energy over time is power × time, expressed in watt-hours or kilowatt-hours.
Series Circuits and Kirchhoff's Voltage Law
A series circuit has a single current path. Consequences:
- Total resistance: Rt = R1 + R2 + R3 … NEETS Mod. 1 §3-2
- Current is identical at every point: It = I1 = I2 = I3
- Source voltage divides across resistors in proportion to their resistance values (voltage divider action): Et = E1 + E2 + E3, where each drop E_n = I × R_n
Kirchhoff's Voltage Law (KVL): The algebraic sum of all voltage drops around any closed loop equals the applied voltage (equivalently, the sum of all voltages around a closed loop is zero).
An open anywhere in a series circuit stops all current. Because no current flows, the full source voltage appears across the open component while all other components read zero volts — the primary troubleshooting indicator for an open in a series path. NEETS Mod. 1 §3-4
A short across one component reads zero volts across itself and redistributes its share of the voltage onto the remaining components.
Parallel Circuits and Kirchhoff's Current Law
A parallel circuit provides two or more current paths between the same two nodes. Consequences:
- The same voltage appears across every branch: Et = E1 = E2 = E3 NEETS Mod. 1 §3-3
- Source current is the sum of branch currents: It = I1 + I2 + I3
- Total resistance is always less than the smallest branch resistance: 1/Rt = 1/R1 + 1/R2 + 1/R3. For two resistors: Rt = (R1 × R2)/(R1 + R2). For N equal resistors: Rt = R/N.
Kirchhoff's Current Law (KCL): The total current entering a junction equals the total current leaving it.
Adding parallel branches lowers total resistance and raises total current drawn from the source. Shipboard power and lighting are wired in parallel so each load receives full system voltage and an open in one branch does not interrupt the others. A short across the supply creates a near-zero-ohm branch that draws enormous current and must be cleared immediately by the circuit's fuse or breaker.
Series-Parallel Circuits and Voltage Dividers
Real circuits combine both configurations. The solution method: reduce parallel groups to single equivalent resistances, then treat those equivalents in series with the remainder, working outward until one total resistance remains. Find total current from the source voltage, then work back inward to find voltage and current at each component.
A voltage divider is a series resistance string tapped at intermediate points to supply several lower voltages from one source. Bleeder current must be large relative to load currents to keep tap voltages stable.
Internal source resistance acts as a series resistor with the load, causing terminal voltage to sag as load current increases — the same mechanism that causes a battery's terminal voltage to drop under a heavy starter load.
RL and RC Time Constants
In a DC inductive circuit, current does not rise instantaneously. The RL time constant is T = L/R seconds. In one time constant, current reaches approximately 63% of its final value; after five time constants it is essentially at full value. The same schedule governs decay when the source is removed. NEETS Mod. 2 §2-2
Inductors in series (not magnetically coupled) add: Lt = L1 + L2 + L3. Inductors in parallel combine by the reciprocal rule, giving a total less than the smallest.
Because current cannot change instantaneously through an inductor, suddenly opening a highly inductive circuit (relay coil, motor winding) can generate a voltage spike many times the supply voltage. Arc-suppression devices and correctly rated contacts are required for this reason.
The RC time constant is T = R × C seconds. In one time constant, the capacitor charges to approximately 63% of the applied voltage; five time constants to essentially full charge. Discharge follows the same curve. NEETS Mod. 2 §3-2
Capacitors combine opposite to resistors: in parallel they add (Ct = C1 + C2 + C3); in series they combine by the reciprocal rule, giving less than the smallest and dividing the applied voltage among them.
A capacitor passes AC but blocks steady DC. A shorted capacitor passes DC and will blow its protection; an open capacitor stops storing charge entirely.
Why It Matters on the Exam
QMED Electrician and Refrigerating Engineer exam questions test these concepts directly and numerically. Expect to:
- Calculate current, voltage, or resistance given the other two using E = I × R. NEETS Mod. 1 §3-1
- Calculate power dissipated in a resistor using P = I²R or P = E²/R, and identify why a conductor overheats.
- Determine total resistance of a series string (sum) or parallel combination (reciprocal rule or product-over-sum). NEETS Mod. 1 §3-2 NEETS Mod. 1 §3-3
- Identify the voltage reading across an open component in a series circuit (full source voltage).
- Distinguish primary from secondary cells and state what fixes cell voltage (chemistry) versus capacity (size). NEETS Mod. 1 §2-1
- State the RL and RC time constant formulas and the 63% / five-time-constant rule. NEETS Mod. 2 §2-2 NEETS Mod. 2 §3-2
- Explain why adding loads to a parallel distribution panel increases total current.
Common Pitfalls
1. Confusing cell voltage with cell size. A larger lead-acid cell is still 2.1 V per cell. Size increases amp-hour capacity only. NEETS Mod. 1 §2-1
2. Adding parallel resistances like series resistances. Parallel total resistance is always less than the smallest branch. Use 1/Rt = 1/R1 + 1/R2 + … or the product-over-sum shortcut for two resistors. NEETS Mod. 1 §3-3
3. Adding parallel capacitances like series capacitances — or vice versa. Capacitors add in parallel and combine by reciprocal in series — the reverse of resistors. NEETS Mod. 2 §3-2
4. Forgetting that an open in a series circuit reads full source voltage. Candidates often expect zero volts across a failed (open) component. In a series circuit with no current flowing, the voltmeter placed across the open reads the full applied EMF. NEETS Mod. 1 §3-2
5. Ignoring internal resistance. A battery that reads normal open-circuit voltage may still be unable to deliver rated current if internal resistance is high. Terminal voltage under load = EMF − (I × r_internal). NEETS Mod. 1 §3-4
6. Misapplying the power formula. P = EI is correct only when E and I are both known. When only current and resistance are known, use P = I²R. When only voltage and resistance are known, use P = E²/R. Using the wrong form with a derived quantity introduces errors. NEETS Mod. 1 §3-1
7. Treating the 63% time-constant rule as applying to 50% or 100%. One time constant = 63% of final value. Full value (for practical purposes) requires five time constants. NEETS Mod. 2 §2-2
Quick Check
Q1 — A circuit has a 24 V source and a single 8 Ω resistor. What is the current, and what power is dissipated?
I = E/R = 24/8 = 3 A. P = I²R = (3)² × 8 = 72 W, or P = EI = 24 × 3 = 72 W. NEETS Mod. 1 §3-1
Q2 — Three resistors of 10 Ω, 20 Ω, and 30 Ω are connected in series across 120 V. What is the voltage drop across the 20 Ω resistor?
Rt = 10 + 20 + 30 = 60 Ω. I = 120/60 = 2 A. E(20 Ω) = 2 × 20 = 40 V. NEETS Mod. 1 §3-2
Q3 — Two resistors, 6 Ω and 12 Ω, are connected in parallel. What is the total resistance?
Rt = (6 × 12)/(6 + 12) = 72/18 = 4 Ω. Note: 4 Ω is less than the smallest branch (6 Ω), confirming the answer is reasonable. NEETS Mod. 1 §3-3
Q4 — A voltmeter placed across one resistor in a series circuit reads the full supply voltage. What does this indicate?
That resistor is open (broken). With no current flowing in the series path, no voltage drops across the good resistors, and the full source EMF appears across the open component. [NEETS Mod. 1 §3-2