# Parallel and Series Circuit

on . Posted in Electrical Engineering

Parallel and series are two different configurations in which electrical components can be connected within a circuit.

### Parallel and Series Circuit Index

• Parallel Configuration  -  In a parallel configuration, electrical components are connected in such a way that they share the same voltage across their terminals.  Each component has its own path for the current to flow.  In a parallel circuit, if one component fails, it does not necessarily affect the operation of the other components.  Examples of parallel connections include household electrical outlets and the wiring in many appliances.
• Characteristics of a parallel circuit:
• Each component has the same voltage across it.
• The total current flowing into the junction splits into separate branches.
• The total resistance decreases as more branches are added.
• Series Configuration  -  In a series configuration, electrical components are connected sequentially, so the same current flows through each component.  The total resistance of the circuit is the sum of the individual resistances.  If one component fails in a series circuit, the entire circuit may fail or be affected, as the current cannot bypass the failed component.  Examples of series connections include Christmas tree lights and flashlight circuits.
• Characteristics of a series circuit:
• The same current flows through each component.
• The total resistance of the circuit is the sum of the individual resistances.
• The total voltage across the circuit is the sum of the voltages across each component.

• Independent Operation  -  Each component operates independently, so if one component fails, it does not necessarily affect the operation of the others.
• Voltage Across Components  -  Each component receives the same voltage across its terminals, ensuring consistent operation.
• Easy to Add or Remove Components  -  Adding or removing components in parallel is relatively simple, as it does not significantly affect the rest of the circuit.
• Increased Reliability  -  Parallel circuits can be more reliable than series circuits because the failure of one component does not disrupt the operation of the entire circuit.
• Higher Current Requirements  -  Parallel circuits may require higher currents, especially when multiple components are connected, which can lead to increased power consumption.
• Complexity in Wiring  -  Parallel circuits often require more complex wiring compared to series circuits, especially in larger systems.
• Costlier  -  Parallel circuits may require more components, leading to higher costs compared to series circuits.
• Overloading Issues  -  If not properly designed, parallel circuits can be prone to overloading, especially if too many components are connected to the same power source.

### Parallel Circuit formulas

$$(1\;/\;R_t) \;=\; (1\;/\;R_1) + (1\;/\;R_2) + (1\;/\;R_3) \; + ... +\; (1\;/\;R_n)$$     (Resistor)

$$C_t \;=\; C_1 + C_2 + C_3 \; + ... + \; C_n$$     (Capacitor)

$$(1\;/\;L_t) \;=\; (1\;/\;L_1) + (1\;/\;L_2) + (1\;/\;L_3) \; + ... +\; (1\;/\;L_n)$$     (Inductor)

Symbol English Metric
$$R$$ = resistance $$\Omega$$ $$kg-m^2\;/\;s^3-A^2$$
$$C$$ = capacitor $$F$$ $$s^4-A^2\;/\;kg-m^2$$
$$L$$ = inductor $$H$$ $$kg-m^2\;/\;s^2-A^2$$

• Simple Wiring  -  Series circuits typically have simpler wiring configurations compared to parallel circuits, making them easier to design and implement.
• Lower Current Requirements  -  Series circuits generally require lower currents compared to parallel circuits, which can lead to lower power consumption.
• Cost-Efficient  -  Series circuits may require fewer components compared to parallel circuits, resulting in lower costs.
• Easy Current Regulation  -  The same current flows through each component in series, making it easier to regulate and control the current in the circuit.
• Dependent Operation  -  Components in a series circuit are dependent on each other, so if one component fails, it can disrupt the operation of the entire circuit.
• Voltage Distribution  -  Voltage is divided among the components in a series circuit, potentially leading to inconsistent performance.
• Increased Total Resistance  -  The total resistance of a series circuit is the sum of the individual resistances, which can lead to higher overall resistance compared to parallel circuits.
• Reduced Reliability  -  Series circuits can be less reliable than parallel circuits because the failure of one component can affect the operation of the entire circuit.

### Series Circuit formulas

$$R_t \;=\; R_1 + R_2 + R_3 \; + ... + \; R_n$$     (Resistor)

$$(1\;/\;C_t) \;=\; (1\;/\;C_1) + (1\;/\;C_2) + (1\;/\;C_3) \; + ... +\; (1\;/\;C_n)$$     (Capacitor)

$$L_t \;=\; L_1 + L_2 + L_3 \; + ... + \; L_n$$     (Inductor)

Symbol English Metric
$$R$$ = resistance $$\Omega$$ $$kg-m^2\;/\;s^3-A^2$$
$$C$$ = capacitor $$F$$ $$s^4-A^2\;/\;kg-m^2$$
$$L$$ = inductor $$H$$ $$kg-m^2\;/\;s^2-A^2$$

The choice between series and parallel configurations depends on various factors such as the specific requirements of the circuit, desired functionality, cost considerations, and reliability concerns.  Each configuration has its own set of advantages and disadvantages that should be carefully considered during the design process.

Tags: Electrical