Current, Voltage, Resistance and Ohm's Law

⚡ Current, Voltage, Resistance and Ohm's Law

Part 1 of 7 — Electricity on the ASVAB

Topic Overview

What Electronics Information (EI) Is

Electronics Information is the 6th subtest on the computer-adaptive CAT-ASVAB, right after Mathematics Knowledge. You get 15 scored questions in 10 minutes, which works out to about 40 seconds per question. Every question has 4 answer choices.

You do not need to be an electrician. EI asks about a small set of ideas that come up again and again:

• the three basic quantities: current, voltage and resistance
• Ohm's law, with numbers simple enough to work by hand (no calculator is allowed)
• which materials conduct electricity and which insulate
• how meters measure a circuit
• series and parallel circuits, components and their symbols, and AC vs DC (the other two EI topics in this course)

Key Fact: EI is not part of your AFQT score (that comes from Arithmetic Reasoning, Mathematics Knowledge, Word Knowledge and Paragraph Comprehension). EI matters for job line scores: for example the Air Force Electronics score (E = GS + AR + MK + EI), the Navy and Marine Corps Electronics score (EL = GS + AR + MK + EI), and the Marine Corps Mechanical Maintenance score (MM = AR + MC + EI + AS). In the Army, EI is one of the subtests that matter most for the Electronics, General Maintenance, Mechanical Maintenance and Surveillance and Communications scores. Ask your recruiter which line scores your target job needs.

If you take the paper version at a test site, EI has 20 questions in 9 minutes. The high-school CEP computer version has 16 EI questions. The content is the same.

The Big Three

Almost every EI question in this topic is about one of three quantities. Learn the name, the letter and the unit of each one.

Two more words you will see:

• A circuit is a complete loop that charge can travel around: a source (like a battery), wires, and a load (something that uses the energy, like a lamp or motor).
• A conductor lets charge flow easily (copper wire); an insulator blocks it (the rubber or plastic coating on the wire).

Key Fact: The letter $I$ stands for current (from the French intensité), not "C" for current. Lock it in now: $I$ = current, in amps.

These three quantities are tied together by Ohm's law, $V = IR$, which you will master in Part 4.

Warm-up: read the circuit. 🎯 These are the kinds of quick questions EI opens with.

Match each quantity to its unit. 🔽

Key Takeaways — Part 1

• EI is the 6th CAT-ASVAB subtest: 15 questions in 10 minutes, about 40 seconds each
• EI is not in the AFQT, but it feeds electronics and mechanical line scores in every branch
• Current ($I$, amperes) is the flow; voltage ($V$ or $E$, volts) is the push; resistance ($R$, ohms, Ω) is the opposition
• A circuit is a complete loop: source → wire → load → back to the source

Up Next: Part 2 — what electric charge is, and how current and voltage really work.

⚡ Current, Voltage, Resistance and Ohm's Law

Part 2 of 7 — Charge, Current and Voltage

Where Electricity Comes From

Everything is made of atoms. An atom has a center (the nucleus) holding protons, which carry a positive (+) charge, and neutrons, which carry no charge. Around the nucleus move electrons, which carry a negative (−) charge.

• Like charges repel (two negatives push apart).
• Opposite charges attract (a negative is pulled toward a positive).

In a metal like copper, the outermost electron of each atom is held loosely. These free electrons can drift from atom to atom. When something pushes them all in the same direction, you have an electric current.

Electric charge is measured in coulombs (C). One coulomb is the charge of a huge number of electrons (about 6 billion billion), so you never count electrons one at a time.

Current: the Flow

Current is the rate at which charge flows past a point. Its unit, the ampere (amp, A), means one coulomb per second:

$I = \frac{Q}{t} \qquad \text{(current = charge} \div \text{time)}$

Example: 20 coulombs pass a point in 4 seconds. The current is 20 ÷ 4 = 5 A.

Voltage: the Push

Voltage is the electrical "pressure" that pushes charge through a circuit. It is also called potential difference or electromotive force (EMF), which is why some formulas write it as $E$ instead of $V$. Its unit is the volt (V).

A battery has a voltage between its two terminals. No voltage, no push, no current, even if the wires are connected.

The water-pipe picture

More pressure pushes more water through the same pipe. In the same way, more voltage pushes more current through the same resistance.

Batteries and Cells

A single cell produces a fixed voltage. A common AA, AAA, C or D flashlight cell gives about 1.5 V, whatever its size (bigger cells last longer, they do not push harder). Stacking cells end to end, positive to negative, adds their voltages:

Batteries supply direct current (DC): the charge always flows the same way around the circuit.

Which Way Does It Flow?

Two conventions exist, and the ASVAB can ask about either one. Read the wording carefully.

The two arrows point in opposite directions, but they describe the same current with the same size in amps.

Worked examples

1. Charge and time. A wire carries 3 A for 10 seconds. How much charge passes? Rearrange $I = \frac{Q}{t}$ to $Q = I \times t = 3 \times 10 = 30$ coulombs.

2. Stacked cells. A flashlight holds three 1.5-V cells end to end. Total voltage: 3 × 1.5 = 4.5 V.

3. Direction. A question says "electrons flow through the lamp from left to right." The conventional current through the lamp is therefore right to left.

Follow the arrows. 🎯

Check the ideas. 🎯

Work it by hand. ✍️

1) 36 coulombs of charge pass a point in 9 seconds. What is the current, in amperes? (number only)

2) A current of 2 A flows for 15 seconds. How many coulombs of charge pass? (number only)

3) A lantern holds eight 1.5-V cells stacked end to end. What is the total voltage, in volts? (number only)

Complete the water-pipe comparison. 🔽

Key Takeaways — Part 2

• Electrons are negative, protons positive; like charges repel, opposite charges attract
• Current = charge per second: $I = \frac{Q}{t}$; 1 ampere = 1 coulomb per second
• Voltage (potential difference, EMF, $E$) is the push; no voltage, no current
• One flashlight cell ≈ 1.5 V whatever its size; cells stacked end to end add their voltages; a car battery ≈ 12 V
• Electron flow goes − to +; conventional current goes + to −

Up Next: Part 3 — resistance, and why copper wire is wrapped in rubber.

⚡ Current, Voltage, Resistance and Ohm's Law

Part 3 of 7 — Resistance, Conductors and Insulators

Resistance

Resistance is the opposition a material gives to the flow of current. It is measured in ohms, written with the Greek letter omega, Ω. When charge is forced through a resistance, some electrical energy turns into heat. That is how a toaster, a space heater and an old-style light bulb filament work.

Every material falls into one of three groups:

The best conductors, in order

1. Silver: the lowest resistance of any common metal, but expensive
2. Copper: almost as good and far cheaper, so it is the most commonly used wire metal
3. Gold: does not corrode, so it coats connectors and contacts
4. Aluminum: lighter and cheaper, used in overhead power lines

Key Fact: "Best conductor" = silver. "Most commonly used conductor in wiring" = copper. The ASVAB likes this distinction.

Pure water is actually a poor conductor, but real water (tap water, sweat, puddles) has dissolved minerals and conducts well enough to be dangerous. Treat any wet surface near electricity as a conductor.

Four Things That Set a Wire's Resistance

Worked example 1. A copper wire has a resistance of 6 Ω. A second copper wire is the same thickness but three times as long. Its resistance is 3 × 6 = 18 Ω.

Worked example 2. A 10-Ω wire is replaced by one of the same material and length but with twice the cross-sectional area. The new resistance is 10 ÷ 2 = 5 Ω.

Wire Gauge

Wire thickness is labeled by gauge. In the American Wire Gauge (AWG) system the rule runs backwards:

• Larger gauge number = thinner wire = more resistance = less current it can carry safely
• Smaller gauge number = thicker wire = less resistance = more current

A wire that is too thin for its current overheats, which can melt insulation and start a fire. That is why the circuit breaker on each circuit is matched to the wire size.

Key Fact: 10-gauge wire is thicker than 14-gauge wire. If you remember only one thing about gauge, remember that the numbers run backwards.

Compare the wires. 🎯 All four are copper at the same temperature.

Materials and gauge. 🎯

Classify each material. 🔽

Scale the resistance. ✍️ Same material and temperature in each case.

1) A wire has 4 Ω of resistance. A wire of the same thickness but twice as long has how many ohms? (number only)

2) A wire has 12 Ω of resistance. A wire of the same length with three times the cross-sectional area has how many ohms? (number only)

3) A wire has 8 Ω of resistance. A wire half as long and twice the cross-sectional area has how many ohms? (number only)

Key Takeaways — Part 3

• Resistance (Ω) opposes current and turns electrical energy into heat
• Conductors: silver (best), copper (most used), gold (no corrosion), aluminum (light). Insulators: rubber, glass, plastic, porcelain, mica, dry wood. Semiconductors: silicon, germanium
• Longer wire → more resistance; thicker wire → less; hotter metal → more
• Wire gauge runs backwards: bigger number = thinner wire = less current capacity

Up Next: Part 4 — Ohm's law, the one formula that ties current, voltage and resistance together.

⚡ Current, Voltage, Resistance and Ohm's Law

Part 4 of 7 — Ohm's Law

One Formula, Three Forms

Ohm's law says the voltage across a resistance equals the current through it times the resistance:

$V = I \times R$

Rearranged, it gives all three quantities:

The triangle trick

Draw the triangle in Figure 4 on your scratch paper at the start of EI. Cover the letter you want to find:

• Cover V: $I$ and $R$ sit side by side, so multiply: $V = I \times R$
• Cover I: $V$ sits over $R$, so divide: $I = V \div R$
• Cover R: $V$ sits over $I$, so divide: $R = V \div I$

Some books write $E = I \times R$ (with $E$ for EMF). It is the same law.

Worked Examples

1. Find the current. A 12-V battery is connected across a 4-Ω resistor. $I = \frac{V}{R} = \frac{12}{4} = 3$, so the current is 3 A.

2. Find the voltage. A current of 2 A flows through a 6-Ω resistor. $V = I \times R = 2 \times 6 = 12$, so the voltage across it is 12 V.

3. Find the resistance. A heater draws 10 A from a 120-V outlet. $R = \frac{V}{I} = \frac{120}{10} = 12$, so its resistance is 12 Ω.

4. Watch the prefixes. A 9-V battery is connected across a 3-kΩ resistor (k = kilo = 1,000, so 3,000 Ω). $I = \frac{9}{3000} = 0.003$ A = 3 mA (milliamps). Shortcut: volts ÷ kilohms = milliamps, so 9 ÷ 3 = 3 mA.

Reasoning Without Numbers

Many EI questions ask what happens instead of asking for a number. Use $I = \frac{V}{R}$:

Key Fact: Current goes up with voltage and down with resistance. If your answer says more resistance gives more current, you have the formula upside down.

Use the circuit above. ✍️

1) What current flows through the resistor, in amperes? (number only)

2) The 8-Ω resistor is replaced with a 4-Ω resistor. What current flows now, in amperes? (number only)

3) With the original 8-Ω resistor back in place, the battery is replaced with a 12-V battery. What current flows, in amperes? (number only)

Pick the right form. ✍️

1) A current of 5 A flows through a 20-Ω resistor. What is the voltage across it, in volts? (number only)

2) A lamp draws 0.5 A when connected to 6 V. What is its resistance, in ohms? (number only)

3) A 15-V source is connected across a 5-kΩ resistor. What is the current, in milliamps? (number only)

Reason it out. 🎯

Choose the operation. 🔽

Key Takeaways — Part 4

• Ohm's law: $V = I \times R$, so $I = \frac{V}{R}$ and $R = \frac{V}{I}$ (also written $E = IR$)
• Draw the V over I × R triangle on your scratch paper and cover the unknown
• Current rises with voltage and falls with resistance
• Volts ÷ kilohms = milliamps; convert prefixes before you divide

Up Next: Part 5 — how meters measure current, voltage and resistance, and the unit prefixes you need.

⚡ Current, Voltage, Resistance and Ohm's Law

Part 5 of 7 — Measuring Electricity: Meters and Units

Three Meters, Three Jobs

A multimeter is one handheld tool that switches between all three jobs (and usually more). A galvanometer is a very sensitive meter that detects tiny currents; it is the heart of older needle-style meters. A wattmeter measures power.

Why the hookup matters

• An ammeter connected across a part (in parallel) offers a nearly zero-resistance path, so a huge current rushes through it. That can blow the meter's fuse or damage it.
• An ohmmeter connected to a live circuit gives a false reading and can be damaged, because the circuit's voltage adds to the meter's own battery.

Reading an ohmmeter

Key Fact: Checking whether a fuse or bulb is good is a continuity test with an ohmmeter: near 0 Ω means good, infinite means open (bad).

Read the hookup. 🎯

Unit Prefixes

Electronics uses very large and very small numbers, so units get prefixes.

Watch capital vs lowercase: M (mega, a million) and m (milli, a thousandth) differ by a factor of a billion.

Converting

• Larger unit → smaller unit: multiply by 1,000 per step. 3.2 A = 3,200 mA.
• Smaller unit → larger unit: divide by 1,000 per step. 1,500 Ω = 1.5 kΩ.

Symbols you will see in questions

Meters in practice. 🎯

Convert the units. ✍️ Numbers only.

1) 0.75 A = how many milliamps?

2) 6,800 Ω = how many kilohms?

3) 2.5 MΩ = how many kilohms?

Choose the meter and the hookup. 🔽

Key Takeaways — Part 5

• Ammeter: current, in series, low resistance. Voltmeter: voltage, in parallel (across), high resistance. Ohmmeter: resistance, power off
• A multimeter does all three; a galvanometer detects small currents; a wattmeter measures power
• Ohmmeter: about 0 Ω = continuity; infinite = open (blown fuse, broken wire, dead bulb)
• M = million, k = thousand, m = thousandth, µ = millionth

Up Next: Part 6 — how to work EI questions fast and the traps that cost points.

⚡ Current, Voltage, Resistance and Ohm's Law

Part 6 of 7 — EI Test Strategy and Common Traps

Your Time Budget

Most EI questions are recall: you either know that resistance is measured in ohms or you don't. Those should take 10 to 15 seconds. That banks time for the few calculation questions (Ohm's law, unit conversions), which may need 45 to 60 seconds.

How the CAT works for you (and against you)

• You cannot go back to a question once you answer it, and you must answer to move on. Settle each one before you click.
• Some questions may be unscored tryout items. You can't tell which, so treat every question as if it counts.
• If time runs out, unanswered questions are scored as if you guessed at random, and a run of wrong answers at the end of a subtest is penalized heavily. If you are running short, keep reading and genuinely answering rather than clicking randomly.
• No calculator. The numbers are chosen to work by hand.

A four-step routine for calculation questions

1. Name the unknown and its unit (amps? ohms? volts?).
2. Cover it on the triangle you drew on your scratch paper: multiply or divide.
3. Convert prefixes first (kΩ, mA) so the units match.
4. Sanity check: more resistance should mean less current; the answer's unit must match the question.

The Traps That Cost Points

Elimination

When you are unsure, cross out choices with the wrong unit or the wrong direction of change first. In a "what happens to the current" question, two choices usually go the wrong way; the answer is between the other two.

Spot the trap. 🎯 Each question is built around one of the traps above.

Sanity-check the direction of change. 🔽 Use $I = \frac{V}{R}$.

Key Takeaways — Part 6

• CAT EI: 15 questions, 10 minutes, about 40 s each; spend 10–15 s on recall items to bank time for calculations
• No going back and no calculator; treat every question as scored and keep genuinely answering if time runs short
• Routine: name the unknown → cover it on the triangle → convert prefixes → sanity-check the direction
• Know the traps: $E$ = voltage, gauge runs backwards, silver is best but copper is most used, ammeter in series

Up Next: Part 7 — a mixed mastery set at ASVAB difficulty.

⚡ Current, Voltage, Resistance and Ohm's Law

Part 7 of 7 — Mixed Mastery Set

Ten questions at real EI difficulty: a mix of recall, reasoning and hand calculation, in no particular order, just like the test. Give yourself about 40 seconds each. Use scratch paper, no calculator.

Question 1. 🎯

Questions 2–5. 🎯

Questions 6–9. 🎯

Question 10. ✍️ Numbers only.

1) A current of 0.2 A flows through a 50-Ω resistor. What is the voltage across it, in volts?

2) A space heater draws 12 A on a 120-V circuit. What is its resistance, in ohms?

Key Takeaways — Current, Voltage, Resistance and Ohm's Law

• Current (A) = charge per second; voltage (V, also $E$) = the push; resistance (Ω) = the opposition
• Ohm's law: $V = IR$, $I = \frac{V}{R}$, $R = \frac{V}{I}$; current rises with voltage and falls with resistance
• Silver is the best conductor, copper the most used; rubber, glass, porcelain and plastic insulate; silicon and germanium are semiconductors
• Longer or thinner wire → more resistance; bigger gauge number → thinner wire
• Ammeter in series, voltmeter across, ohmmeter power off; 0 Ω = continuity, infinite = open

Next topic: Series and Parallel Circuits and Power.