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Series vs Parallel Circuits
Equivalent Resistance, Current Paths, and Voltage Division
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Electric circuits can be connected in different ways, and the two most common patterns are series and parallel. In a series circuit, components are arranged in one continuous loop, so the same current passes through each part. In a parallel circuit, components are connected on separate branches, giving current more than one path to follow. Understanding the difference matters because it explains how lights, batteries, and household wiring behave.
The key ideas are how current, voltage, and resistance are shared in each type of circuit. In series, resistances add directly and the total current usually decreases as more devices are added. In parallel, each branch gets the full source voltage, and the total current is the sum of the branch currents. These patterns help predict bulb brightness, battery drain, and what happens when one component fails.
Key Facts
- Series circuit: I_total = I1 = I2 = I3
- Parallel circuit: V_total = V1 = V2 = V3
- Series resistance: R_total = R1 + R2 + R3
- Parallel resistance: 1/R_total = 1/R1 + 1/R2 + 1/R3
- Ohm's law: V = IR
- Parallel current adds: I_total = I1 + I2 + I3
Vocabulary
- Series circuit
- A circuit in which components are connected one after another in a single path for current.
- Parallel circuit
- A circuit in which components are connected on separate branches so current has multiple paths.
- Current
- Current is the rate at which electric charge flows through a circuit, measured in amperes.
- Voltage
- Voltage is the electric potential difference that pushes charge through a circuit, measured in volts.
- Resistance
- Resistance is the opposition to current flow in a component, measured in ohms.
Common Mistakes to Avoid
- Assuming current is always the same everywhere in any circuit, which is wrong because current splits between branches in a parallel circuit and only stays the same through all components in series.
- Adding voltages across branches in a parallel circuit, which is wrong because each branch has the same voltage as the source rather than a summed voltage.
- Thinking adding more bulbs always makes total resistance larger, which is wrong because resistance increases in series but decreases when equal resistors are added in parallel.
- Believing one burned out bulb turns off every bulb, which is wrong because that happens in a simple series circuit but not in a parallel circuit where other branches can still work.
Practice Questions
- 1 Three 2 ohm resistors are connected in series to a 12 V battery. Find the total resistance and the current in the circuit.
- 2 Two resistors, 6 ohm and 3 ohm, are connected in parallel across a 12 V battery. Find the equivalent resistance and the total current.
- 3 A house uses parallel wiring for lamps and appliances. Explain why parallel wiring is more practical than series wiring when one device is switched off or fails.