Series and Parallel Circuits

When constructing electrical circuits, there are two primary configurations for arranging components: series and parallel.
These two arrangements use the same types of components but result in different electrical properties and behaviors.

Definition: A series circuit is defined as an arrangement that has a single path for the electric current to pass through.
Electron Flow: In a series circuit, all electrons must pass through every component within the circuit sequence.
Current Behavior: The electrical current ( $I$ ) remains the same at every point in a series circuit. There is no splitting of flow; the magnitude of current measured at the start is identical to the current at any subsequent point.
Voltage Behavior: The voltage ( $V$ ) is shared across each component in the circuit. The sum of the individual voltages across each component is equal to the total voltage supplied by the power source.
Circuit Analysis Example:
- Given a supply voltage of $9\,V$ and a total current of $2\,A$ .
- In a series configuration with two lamps, the current ( $I$ ) passing through lamp one and lamp two will both be $2\,A$ .
- The voltage across the lamps will be split (e.g., if the lamps are identical, each would receive $4.5\,V$ ).

Definition: A parallel circuit is an arrangement where the electric current is split across one or more pathways, referred to as branches.
Electron Flow: Electrons are divided among the available branches so that only a portion of the total flow passes through any single branch.
Current Behavior: The total current flowing from the power source is equal to the sum of the current found in each of the individual branches. Current splits proportionally based on the resistance present on each branch.
Voltage Behavior: The voltage across each individual branch is the same as the total voltage supplied to the circuit. Each branch receives the full potential difference of the source.
Circuit Analysis Example:
- Given a supply voltage of $9\,V$ and a total current of $2\,A$ .
- In a parallel configuration with two branches, the voltage across each branch will be exactly $9\,V$ .
- The current ( $I$ ) will split between the branches (e.g., if branches have equal resistance, each would receive $1\,A$ ), such that the sum equals the total current of $2\,A$ .

Current ( $I$ ):
- Series: Constant throughout the entire loop ( $I_{total} = I_1 = I_2 = I_3...$ ).
- Parallel: Cumulative; the total is the sum of all branch currents ( $I_{total} = I_1 + I_2 + I_3...$ ).
Voltage ( $V$ ):
- Series: Distributed; the total voltage is the sum of the potential drops across components ( $V_{total} = V_1 + V_2 + V_3...$ ).
- Parallel: Constant; every branch experiences the same potential difference ( $V_{total} = V_1 = V_2 = V_3...$ ).

Evaluating a circuit design requires checking it against specific functional requirements.

Design Scenario: A circuit must contain four lamps and one switch, where two lamps are twice as bright as the other two lamps.
Evaluation Criteria: To achieve different brightness levels in identical lamps, the power delivered to them must differ. Since brightness depends on the current and voltage, the circuit must be designed to distribute these values unequally.
Brightness Factors: In identical lamps, a higher current or higher voltage results in greater brightness.
Proposed Logic: To make two lamps brighter than the others, one could use a combination (mixed) circuit. Lamps in a parallel branch with lower resistance or lamps configured to receive a higher share of the total voltage will appear brighter.
Evaluation of Design: A design fails if it places all four lamps in a simple series or simple parallel arrangement with identical components, as this would cause all lamps to have equal brightness. A successful design must manipulate the current flow through specific branches or the voltage drop across specific components.

General Knowledge:
- Understand the definition of a series circuit and a parallel circuit.
- Describe the specific differences in how electricity behaves in each configuration.
- Identify the advantages and limitations inherent to different circuit designs.
Technical Mastery:
- Recall the patterns of current flow ( $I$ ) in both circuit types.
- Explain the mechanisms of voltage ( $V$ ) sharing across components.
- Apply this knowledge to evaluate or propose electrical circuit designs based on specific performance requirements (such as relative brightness).