Series and Parallel Circuits

This section covers the construction and analysis of series and parallel circuits. Understanding these circuit configurations is fundamental to electricity and electronics.

Series Circuits

Definition

In a series circuit, components are connected end-to-end, forming a single path for the current. The current is the same through all components in a series circuit.

Characteristics

• Current (I) is the same through all components.
• The total resistance (R_total) is the sum of the individual resistances.
• The voltage (V) is divided across the components.

Mathematical Relationships

For a series circuit:

1. $R_{total} = R_1 + R_2 + R_3 + ...$
2. $V_{total} = V_1 + V_2 + V_3 + ...$
3. $I_{total} = I_1 = I_2 = I_3 = ...$

Example

Component	Resistance (Ω)	Voltage Drop (V)	Current (A)
Resistor 1	$R_1$	$V_1$	$I$
Resistor 2	$R_2$	$V_2$	$I$
Resistor 3	$R_3$	$V_3$	$I$

Parallel Circuits

Definition

In a parallel circuit, components are connected across each other, providing multiple paths for the current. The voltage is the same across all components in a parallel circuit.

Characteristics

• Voltage (V) is the same across all components.
• The total resistance (R_total) is less than the smallest individual resistance.
• The current divides between the branches.

Mathematical Relationships

For a parallel circuit:

1. $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + ...$
2. $V_{total} = V_1 = V_2 = V_3 = ...$
3. $I_{total} = I_1 + I_2 + I_3 + ...$

Example

Component	Resistance (Ω)	Voltage (V)	Current (A)
Resistor 1	$R_1$	$V$	$I_1$
Resistor 2	$R_2$	$V$	$I_2$
Resistor 3	$R_3$	$V$	$I_3$

Calculating Total Resistance and Current

Understanding how to calculate the total resistance and total current in series and parallel circuits is crucial. These calculations involve applying the appropriate formulas based on the circuit configuration.

Series Circuit - Total Resistance

The total resistance in a series circuit is simply the sum of the individual resistances.

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

Parallel Circuit - Total Resistance

The reciprocal of the total resistance in a parallel circuit is the sum of the reciprocals of the individual resistances.

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

Parallel Circuit - Total Current

The total current in a parallel circuit is the sum of the currents flowing through each branch.

$I_{total} = I_1 + I_2 + I_3 + ...$

Applications

Series and parallel circuits are used in a wide variety of applications, including:

• Christmas lights: Series circuits are used in older Christmas lights. If one bulb fails, the entire string goes out.
• Household wiring: Parallel circuits are used in household wiring. If one appliance is switched off, the others continue to work.
• Dividing voltage: Parallel combinations of resistors can be used to divide a voltage into smaller portions.
• Ensuring correct current: Series combinations of resistors can be used to limit the current in a circuit.