By Lee Johnson, Updated Mar 24, 2022

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The Basics of Electrical Circuits

Electricity requires a complete loop to flow. A circuit is a closed conductive path that allows electrons to travel from a power source—such as a battery—to a device (resistor, light bulb, etc.) and back. Breaking the loop with a switch stops the current and turns off the device.

Key terms:

• Voltage difference: The electrical potential energy per unit charge between two points. For example, a 5‑V battery provides a 5‑volt potential difference between its terminals (1 V = 1 J/C).
• Current: The flow of charge, measured in amperes (A). One ampere equals one coulomb of charge per second.
• Resistance: Opposition to current flow, measured in ohms (Ω). A conductor with 1 Ω of resistance across 1 V will allow 1 A of current.

Ohm’s Law links these quantities: V = I × R.

Series vs. Parallel Circuits

Components can be arranged in two primary ways:

• Series: All components lie along a single path. The same current passes through each component sequentially.
• Parallel: The path splits into multiple branches, each carrying part of the total current. The voltage across each branch is the same.

In a series circuit, the total resistance is the sum of individual resistances:

R_total = R₁ + R₂ + R₃ + …

Example: For resistors 2 Ω, 4 Ω, and 6 Ω in series, the total resistance is 12 Ω.

In a parallel circuit, the reciprocal of the total resistance equals the sum of reciprocals of each resistance:

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + …

Example: For the same resistors in parallel, the calculation yields a total resistance of approximately 1.09 Ω.

Solving Mixed Series–Parallel Circuits

Complex circuits often combine series and parallel sections. Break the circuit into manageable parts, compute each part’s resistance, and then combine them.

Illustration: Three parallel branches, where one branch contains three series resistors (12 Ω, 5 Ω, 3 Ω). The series branch totals 20 Ω. With the other branches at 40 Ω and 10 Ω, the overall resistance is about 5.7 Ω.

Capacitance in Series and Parallel

Capacitance behaves oppositely to resistance:

• Series: 1/C_total = 1/C₁ + 1/C₂ + …, then invert to find C_total.
• Parallel: C_total = C₁ + C₂ + …

The same approach—analyze, simplify, combine—applies to all circuit calculations.

Key Takeaways

• Series circuits: add resistances; parallel circuits: add conductances (reciprocals).
• Use Ohm’s Law for voltage, current, and resistance relationships.
• Decompose complex networks into simpler series and parallel groups.
• Capacitance calculations mirror resistance but with reciprocal relationships in series.