Series and Parallel Circuits

Current in Series Circuits

In a series circuit, components are connected one after the other, forming a single path for the current. This means the same current flows through every component in the circuit.

This is because the total current flowing into the series circuit must equal the total current flowing out. Since there's only one path, the current is undiminished as it passes through each component.

• The current is constant throughout the circuit.
• If one component's resistance increases, the current in the entire circuit will decrease.
• If one component is removed from a series circuit, the circuit is broken and the current stops flowing.

Example

Consider a series circuit with a 12V battery and two resistors, R1 and R2, connected in series. The current flowing through R1 will be the same as the current flowing through R2.

Current in Parallel Circuits

In a parallel circuit, components are connected across each other, providing multiple paths for the current to flow. The total current flowing from the power source is divided among these different paths.

The amount of current flowing through each branch of a parallel circuit depends on the resistance of that branch. Lower resistance branches will allow more current to flow.

• The total current is the sum of the currents in each branch.
• If one component is removed from a parallel circuit, the other components continue to function normally.
• If one component's resistance increases, the total current in the circuit will decrease.

Mathematical Relationship - Series Circuits

In a series circuit, the total resistance ($R_{total}$) is the sum of the individual resistances:

$$R_{total} = R_1 + R_2 + R_3 + ...$$

The current ($I$) in a series circuit is the same through all components and can be calculated using Ohm's Law:

$$I = \frac{V}{R_{total}}$$

Where:

• $V$ is the voltage of the power source.
• $R_{total}$ is the total resistance of the circuit.

Mathematical Relationship - Parallel Circuits

In a parallel circuit, the reciprocal of the total resistance ($R_{total}$) is the sum of the reciprocals of the individual resistances:

$$\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$$

The total current ($I$) in a parallel circuit is the sum of the currents in each branch:

$$I = I_1 + I_2 + I_3 + ...$$

The voltage ($V$) across each parallel branch is the same as the voltage of the power source:

$$V_1 = V_2 = V_3 = ... = V$$

Table Summarizing Key Differences

Feature	Series Circuit	Parallel Circuit
Current	Same through all components	Divided among branches
Voltage	Divides across components	Same across all branches
Resistance	Total resistance increases	Total resistance decreases
Path for Current	Single path	Multiple paths