🔌 Series and Parallel Circuits and Power

Part 1 of 7 — Circuits on the ASVAB

Topic Overview

Why Circuits Matter on EI

Electronics Information gives you 15 questions in 10 minutes on the CAT-ASVAB (about 40 seconds each). Circuit questions are some of the most common: a small diagram of a battery, some resistors or bulbs, maybe a switch, and a question like "what is the current?" or "which bulbs stay lit?" The numbers are always simple enough to do without a calculator.

You will use Ohm's law constantly in this topic:

$V = I \times R \qquad I = \frac{V}{R} \qquad R = \frac{V}{I}$

(If that is new, work through the topic Current, Voltage, Resistance and Ohm's Law first.)

The Parts of Every Circuit

🔌 Series and Parallel Circuits and Power

Part 2 of 7 — Series Circuits

One Path Only

In a series circuit, the parts are connected end to end, so there is only one path for current. Every electron that leaves the battery passes through every part, one after another.

The Three Series Rules

The voltage "drop" across each part follows Ohm's law, $V = I \times R$. Since the current is the same in every part, the biggest resistor gets the biggest share of the voltage.

What Happens When Things Change

• Add another resistor in series: total resistance goes up, so the current goes down (every bulb in the string dims).
• One part burns out or a wire breaks: the only path is broken, so everything goes off. This is the classic behavior of older holiday light strings: one dead bulb and the whole string goes dark.
• A switch or fuse is always placed in series with what it controls or protects, because it has to be able to break the one path.

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Part 3 of 7 — Parallel Circuits

Several Paths

In a parallel circuit, each part is connected directly across the source, on its own branch. Current leaving the battery splits at a junction, each share goes through one branch, and the shares rejoin before returning to the battery.

The Three Parallel Rules

Each branch follows Ohm's law on its own: $I_{branch} = \frac{V_{source}}{R_{branch}}$. The smallest resistance carries the largest current.

What Happens When Things Change

• One branch burns out or is switched off: the other branches still have a complete path to the battery, so they stay on at the same brightness.
• Add another branch: total resistance goes down, so the total current from the source goes up (each existing branch keeps its own current).

Key Fact: Your home is wired in parallel. Every outlet and light gets the full household voltage, and turning off the kitchen light does not turn off the TV.

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Part 4 of 7 — Combination Circuits and Circuit Faults

Series-Parallel Circuits

Many diagrams mix the two: a resistor in series with a parallel group. Solve them by shrinking the circuit one piece at a time.

1. Find a group that is purely parallel (or purely series) and replace it with its equivalent resistance.
2. Repeat until one resistance is left. That is the total.
3. Total current = source voltage ÷ total resistance.
4. Work back out using Ohm's law for each piece.

Worked example (Figure 4, coming up)

A 4-Ω resistor is in series with a parallel pair of 6 Ω and 12 Ω, across 24 V.

• Parallel pair: $\frac{6 \times 12}{6 + 12} = \frac{72}{18} = 4$ Ω.
• Total: $4 + 4 = 8$ Ω (the series resistor plus the pair).
• Total current: $\frac{24}{8} = 3$ A. All 3 A flows through the 4-Ω series resistor.
• Voltage across the series resistor: $3 \times 4 = 12$ V. That leaves $24 - 12 = 12$ V across the parallel pair.
• Branch currents: $\frac{12}{6} = 2$ A and $\frac{12}{12} = 1$ A, which add back to 3 A. ✓

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Part 5 of 7 — Electrical Power and Energy

What Power Means

Power is how fast electrical energy is used (or delivered). It is measured in watts (W). A 100-W bulb uses energy twice as fast as a 50-W bulb. 1 kilowatt (kW) = 1,000 W.

The Power Formula

$P = I \times V \qquad \text{(watts = amps} \times \text{volts)}$

Combine it with Ohm's law and you get two more forms, useful when you know the resistance:

Rearranged: $I = \frac{P}{V}$ (find the current an appliance draws) and $V = \frac{P}{I}$.

Worked example 1. A 1,200-W hair dryer runs on 120 V. Current: $I = \frac{1200}{120} = 10$ A.

Worked example 2. A 60-W bulb on a 120-V circuit. Current: $\frac{60}{120} = 0.5$ A. Resistance: $R = \frac{V}{I} = \frac{120}{0.5} = 240$ Ω.

Key Fact: Resistance turns electrical energy into heat. Doubling the current through the same resistor makes four times the heat ($P = I^2R$). That is why a short circuit, with its huge current, heats wires so fast.

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Part 6 of 7 — Circuit Test Strategy and Common Traps

Timing

On the CAT-ASVAB, EI is 15 questions in 10 minutes: about 40 seconds each. A circuit diagram with numbers usually takes longer than a vocabulary item, so move quickly through recall questions and give diagrams up to about a minute. On the paper test, EI is 20 questions in 9 minutes, so speed matters even more.

You cannot go back on the CAT, and you must answer to move on, so finish each question before you click. Some questions may be unscored tryouts you cannot identify: treat every one as scored. If time is running out, keep working real answers; a string of rushed wrong answers at the end is penalized heavily.

A 20-second first look at any diagram

1. Series or parallel? Trace the path from the + terminal. One path = series. A junction where the wire splits = parallel branches.
2. What does the question ask for? Total resistance, current, a voltage drop, power, or "which bulbs stay lit"?
3. Can you reason instead of calculate? Many questions ask only whether something goes up, down or stays the same.

Fast facts to apply without a formula

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Part 7 of 7 — Mixed Mastery Set

Ten questions mixing everything in this topic, at real EI difficulty. Aim for about 40 seconds each, using scratch paper and no calculator.