Circuits and Ohm's Law: Practice Questions & Explanations

Ohm's Law: V = IR (Voltage = Current × Resistance). Rearranged: I = V/R, or R = V/I. With V = 12, R = 4: I = 12/4 = 3 A. Master these three forms: (1) V = IR (find voltage given current and resistance); (2) I = V/R (find current given voltage and resistance); (3) R = V/I (find resistance given voltage and current). Power equations (often combined with Ohm's Law): P = VI; P = I²R (since V = IR); P = V²/R (since I = V/R). Choose based on what's known. Example: 12V circuit, 4Ω resistance. Current = 3 A (just calculated). Power = VI = 12 × 3 = 36 W; or I²R = 9 × 4 = 36 W; or V²/R = 144/4 = 36 W — all give the same answer. Common ASVAB EI calculations: (1) Find current in a circuit; (2) Find voltage across a resistor; (3) Find resistance needed for desired current; (4) Find power consumption; (5) Total resistance in series/parallel circuits. SERIES circuit: R_total = R₁ + R₂ + R₃ + ... (resistances add); same current through all; voltages add up to source. PARALLEL circuit: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ... (reciprocals add); same voltage across all branches; currents add up to source current. For two parallel resistors: R_total = (R₁ × R₂) / (R₁ + R₂). Parallel resistance is always LESS than the smallest individual resistance.

In a series circuit, total resistance = sum of individual resistances. R_total = 10 + 20 + 30 = 60Ω. Series circuit characteristics: (1) Only ONE PATH for current; (2) Same current through every component; (3) Voltage divides among components (V_total = V₁ + V₂ + V₃); (4) Total resistance = sum of resistances; (5) Failure of one component (e.g., one bulb burning out) breaks the entire circuit; (6) Adding more components increases total resistance, reducing current. Classic example: old Christmas lights — series-wired, one bulb burns out, all go dark. Modern lights are usually parallel. Voltage divider: a common application of series resistors. Two resistors R₁ and R₂ in series across a voltage source V_in. The voltage across R₂ = V_in × R₂/(R₁ + R₂). This 'divides' the voltage proportionally — useful for getting a specific intermediate voltage from a power source. Example: 12V source with R₁ = 1000Ω and R₂ = 2000Ω. Voltage across R₂ = 12 × 2000/3000 = 8V. PARALLEL circuit by contrast: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃ = 1/10 + 1/20 + 1/30 = 6/60 + 3/60 + 2/60 = 11/60. R_total = 60/11 ≈ 5.45Ω. Note this is LESS than the smallest single resistor (10Ω) — that's always true for parallel. ASVAB EI tests both calculations and conceptual differences between series and parallel.

A fuse is a safety device — a thin wire designed to MELT (blow) when current exceeds its rated value, opening the circuit and protecting downstream components from damage. Once blown, the fuse must be REPLACED — single-use device. Types: (1) GLASS TUBE fuses — small, used in electronics, vehicles; (2) BLADE fuses — automotive (typical colors indicate amperage: tan=5A, brown=7.5A, red=10A, blue=15A, yellow=20A, clear=25A, green=30A); (3) AGC/MDL fuses — household; (4) High-voltage / industrial fuses. Ratings: marked with maximum continuous current (e.g., 5A, 10A, 20A); voltage rating (e.g., 250V); response speed (fast-acting vs slow-blow / time-delay — slow-blow tolerates brief startup surges from motors). CIRCUIT BREAKERS are like reusable fuses — they trip when current is too high, but reset by flipping the switch. Used in residential/commercial breaker panels instead of fuses. Modern circuit breakers: thermal (heating element bends), magnetic (electromagnet opens contacts), or combination; GFCI (ground-fault circuit interrupter) detects current imbalance between hot and neutral wires — used in bathrooms, kitchens, outdoors to prevent shocks; AFCI (arc-fault circuit interrupter) detects arcing — used in bedrooms to prevent fires. Replacing fuses: ALWAYS replace with the SAME rating — using a higher-rated fuse defeats the protection and can cause fire or damage; lower-rated fuse will blow repeatedly. Resettable polyfuses (PPTC) in some electronics — increase resistance when hot, recover when cool; reusable but slower response. Surge protectors are different — they protect against voltage spikes, not excess current. NEVER bypass a fuse or breaker — it's there for a reason. Common ASVAB EI safety items address fuse function and proper replacement.

Circuit topologies: SERIES — components connected end-to-end in a single path; only ONE PATH for current; SAME CURRENT through every component; voltage DIVIDES among components (V_total = V₁ + V₂ + V₃...). Resistances ADD (R_total = R₁ + R₂ + R₃). Adding more components increases total resistance, decreases current. Failure of one component (open) breaks the entire circuit. Examples: old Christmas lights (one bulb out = all dark); switches and protective devices in line with loads; voltage divider circuits. PARALLEL — components connected across the same two nodes; MULTIPLE PATHS for current; SAME VOLTAGE across every component; current DIVIDES among branches (I_total = I₁ + I₂ + I₃...). Reciprocal resistances add: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. Total resistance is LESS than smallest individual resistance. Failure of one component does NOT break others. Examples: household wiring (multiple outlets in parallel — one device off doesn't affect others); modern LED Christmas lights; speakers wired in parallel. OPEN CIRCUIT — break in the circuit; no current can flow; infinite resistance. SHORT CIRCUIT — unintended low-resistance path bypassing the load; very high current; can cause damage, fire, or trip breakers. Why parallel for household wiring: each appliance gets full line voltage (120V) regardless of others; turning off one appliance doesn't affect others; failure of one doesn't affect others. Series-parallel combinations: real circuits often combine both; analyze by reducing parallel groups to equivalent resistances, then summing series elements. Kirchhoff's Laws: (1) VOLTAGE LAW (KVL): sum of voltage changes around any closed loop = 0; (2) CURRENT LAW (KCL): sum of currents into any node = sum of currents out. Used to analyze complex circuits. ASVAB EI commonly tests series vs parallel identification and calculation.

Each bulb individually: P = VI, so I = P/V = 60/120 = 0.5 A. In parallel, currents add: total I = 0.5 + 0.5 = 1 A. Verify: total power = 60 + 60 = 120W; P = VI = 120 × 1 = 120W ✓. Parallel circuit principles: (1) SAME VOLTAGE across all branches (each bulb gets full 120V); (2) CURRENTS ADD (total = sum of branch currents); (3) Each branch operates independently — turning one off doesn't affect the other. If the same two bulbs were in SERIES: each would get half the voltage (60V), so each would operate at 1/4 normal brightness (power = V²/R, so half voltage means 1/4 power). Both bulbs would draw the same current. Calculation: each bulb's resistance = V²/P = 120²/60 = 240Ω. In series, total R = 240 + 240 = 480Ω. Current = V/R = 120/480 = 0.25 A. Power dissipated = I²R = 0.0625 × 480 = 30W total (15W per bulb) — far dimmer than rated. This is why household appliances are wired in parallel, not series — each gets full voltage and full power regardless of others. Christmas lights: old-style series-wired light strings each bulb gets a fraction of line voltage (120V/50 bulbs = 2.4V per bulb); when one bulb burns out, the entire string goes out. Modern strings either use parallel wiring or have shunt mechanisms in each bulb that bypass burned-out filaments. LED Christmas lights use LEDs with appropriate series resistors and circuit design. ASVAB EI calculations: practice converting between V, I, R, P using Ohm's Law and Power Law, and applying series/parallel rules. Watts, volts, amps, and ohms are the four fundamental electrical quantities — knowing any two often lets you calculate the others.

In a series circuit, resistances add: R_total = 10 + 20 + 30 = 60 Ω.

Power = Voltage × Current = 110 × 5 = 550 watts.

PARALLEL CIRCUIT CURRENT DISTRIBUTION: In a parallel circuit, ALL branches share the SAME VOLTAGE (equal to the supply voltage). Current in each branch is determined by Ohm's Law: I = V/R. The 10Ω branch has the lowest resistance, so with the same voltage applied, it carries the most current (twice as much as each 20Ω branch). This is why fuses and circuit breakers are connected in series — if resistance drops (short circuit), current in that branch increases dramatically, blowing the fuse.

In a SERIES CIRCUIT, if one component burns out, the ENTIRE circuit stops working because there's only ONE path for current — breaking it anywhere stops all flow (like old Christmas lights where one bad bulb killed the whole string). ASVAB Electronics Information tests circuit types. SERIES: components in a single path; same current through all; if one breaks, all stop. PARALLEL: multiple paths; if one branch breaks, others keep working (like household wiring). Knowing that a break anywhere in a series circuit stops everything (vs parallel) is commonly tested.

In a PARALLEL circuit, the VOLTAGE is the SAME across each parallel branch (each branch gets the full source voltage). ASVAB Electronics Information tests circuit types. PARALLEL CIRCUITS: same voltage across each branch; current divides among branches; total resistance is LESS than the smallest individual resistance; if one branch fails, others keep working. SERIES CIRCUITS: same current through all; voltage divides among components. Household wiring is parallel (so each outlet gets full voltage and devices work independently). Knowing voltage is equal across parallel branches is commonly tested.

Ohm's law states V = I × R, where V is voltage, I is current, and R is resistance. To find current, rearrange to I = V ÷ R. Here I = 12 volts ÷ 4 ohms = 3 amps. Ohm's law is the single most important relationship in basic electronics, and you should be able to solve for any of the three variables: V = IR, I = V/R, and R = V/I. A common error is multiplying instead of dividing (12 × 4 = 48). The current in this circuit is 3 amperes.

In a series circuit, the components are connected end to end in a single path, so the total resistance is simply the sum of the individual resistances: R_total = R1 + R2 + R3. The same current flows through every component in series, while the voltage divides among them. This contrasts with a parallel circuit, where total resistance is found with a reciprocal formula and is always less than the smallest individual resistor. Recognizing series (add resistances, one path) versus parallel (multiple paths, lower total resistance) is essential circuit knowledge.

In a series circuit there is only one path for current to flow. If one bulb burns out, it breaks the path (creates an open circuit), so current can no longer flow and all the bulbs go out. This is the classic problem with old-style series holiday lights. In a parallel circuit, by contrast, each bulb has its own path, so one burning out does not affect the others — which is why modern wiring and most household circuits use parallel connections. The behavior when one component fails is a key way to tell series from parallel.

In a parallel circuit, the total (equivalent) resistance is always less than the smallest individual resistor because adding more parallel paths gives the current more ways to flow, reducing overall resistance. The total is found with the reciprocal formula 1/R_total = 1/R1 + 1/R2 + ... This contrasts sharply with a series circuit, where resistances add up and the total is larger than any single resistor. Remembering that parallel lowers total resistance (more paths) while series raises it (one path) is a frequently tested circuit concept.