19.3 Parallel Circuits
3 min read•june 25, 2024
Parallel circuits offer multiple paths for current flow, keeping voltage constant across branches while dividing current. This setup allows for safer connections of components with different voltage ratings and enables flexible circuit designs.
Calculating in parallel circuits involves reciprocals, unlike series circuits. ###'s_Law_0### applies to each independently, making it easier to analyze current and power distribution across the circuit's components.
Parallel Circuits
Analysis of parallel circuit diagrams
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- Parallel circuits provide multiple paths for current to flow through
- Each path in a is called a branch, allowing current to split and flow through different components simultaneously
- Voltage remains constant across each branch in a parallel circuit, ensuring that all components connected in parallel experience the same potential difference
- Current divides at each in a parallel circuit and recombines at the other end
- Total current in a parallel circuit is calculated by summing the currents flowing through each individual branch:
- Resistors connected in parallel have the same across them
- Voltage across each in a parallel circuit is equal to the source voltage, regardless of the resistor's value:
- This property allows components with different voltage ratings to be safely connected in parallel (LED arrays)
Equivalent resistance in circuit combinations
- Equivalent resistance () represents the single resistance value that can replace a combination of resistors while maintaining the same overall current and voltage characteristics
- For resistors connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances:
- Simplified formula for calculating the equivalent resistance of two resistors in parallel:
- Connecting resistors in parallel decreases the overall resistance, allowing more current to flow (parallel battery configurations)
- For resistors connected in series, the equivalent resistance is calculated by summing the individual resistances:
- Complex circuits with combinations of series and parallel resistors can be simplified by calculating the equivalent resistance of each parallel or series section, then combining the resulting equivalent resistances
- This process is repeated until the circuit is reduced to a single equivalent resistance ( circuits)
- The inverse of resistance, , is often used in parallel circuit calculations to simplify the process of finding equivalent resistance
Ohm's law for parallel circuits
- Ohm's law describes the relationship between voltage, current, and resistance in a circuit:
- represents voltage measured in volts (V)
- represents current measured in amperes (A)
- represents resistance measured in ohms ()
- In parallel circuits, Ohm's law can be applied to each branch independently
- Current flowing through each branch is calculated using the formula: , where is the source voltage and is the resistance of the specific branch
- Total current in a parallel circuit is determined by summing the currents flowing through each branch:
- Power dissipated by each resistor in a parallel circuit is calculated using the formula:
- Total power dissipated in a parallel circuit is the sum of the power dissipated by each individual resistor:
- Power calculations are essential for determining the proper ratings for components in a circuit (resistors, light bulbs)
Circuit Analysis Techniques
- is used to solve for voltages at specific points in a circuit by applying
- involves solving for currents in closed loops of a circuit using Kirchhoff's Voltage Law
- and are powerful tools for simplifying complex circuits into equivalent circuits, making analysis easier
Key Terms to Review (25)
$I_{total}$: $I_{total}$ is the total current in a parallel circuit, which is the sum of the individual currents flowing through each branch. It represents the total amount of electric charge flowing through the circuit per unit of time, and is a fundamental concept in understanding the behavior of parallel circuits.
$R_{eq}$: $R_{eq}$ is the equivalent resistance in a parallel circuit, which represents the combined resistance of all the parallel branches. It is a crucial concept in understanding the behavior and analysis of parallel electrical circuits.
$V = IR$: $V = IR$ is a fundamental equation in electrical engineering that describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. This equation is a cornerstone of understanding how electrical systems function and is essential for analyzing and designing various electrical circuits.
Ampere: The ampere (symbol: A) is the base unit of electric current in the International System of Units (SI). It is the constant flow of one coulomb of electrical charge per second and is a fundamental measure of the strength of an electric current.
Branch: A branch is a division or subdivision of a main circuit or system that provides an alternate path for the flow of electrical current. It is a crucial concept in the context of parallel circuits, allowing for the distribution and control of electrical energy.
Capacitor: A capacitor is a passive electronic component that stores electrical energy in an electric field. It is composed of two conductors separated by an insulator and is used in various electrical and electronic circuits to block DC signals, filter signals, and store energy.
Conductance: Conductance is a measure of a material's ability to allow the flow of electric current. It is the reciprocal of resistance and represents the ease with which electric charge can move through a conductor, such as a wire or a resistor in a parallel circuit.
Current Division: Current division is the principle that describes how electric current is distributed across parallel branches in a circuit. It states that the current through each branch is inversely proportional to the resistance of that branch, allowing the current to 'divide' across the parallel paths.
Equivalent Resistance: Equivalent resistance is the single resistance value that can replace a network of resistors to produce the same current and voltage relationships as the original network. It is a fundamental concept in the analysis of electrical circuits, particularly in the context of series and parallel circuits.
Junction: A junction is a point where two or more electrical conductors meet and connect, allowing the flow of electric current between them. Junctions are essential components in various electrical circuits, particularly in the context of parallel circuits.
Kirchhoff's Current Law: Kirchhoff's Current Law states that the sum of all the currents entering and leaving a node (a point where multiple circuit elements are connected) must be zero. This law is based on the principle of conservation of charge, which states that charge cannot be created or destroyed in an electrical circuit.
LED Array: An LED array is a collection of multiple light-emitting diodes (LEDs) arranged in a specific pattern or configuration to produce a desired lighting effect. These arrays are commonly used in various applications, such as displays, lighting systems, and indicators, where the combined output of the individual LEDs can create a more powerful or diverse light source.
Mesh Analysis: Mesh analysis is a method used in electrical circuit analysis to determine the currents flowing through each branch of a circuit. It involves setting up a system of linear equations based on the application of Kirchhoff's voltage law around each independent loop or mesh of the circuit.
Nodal Analysis: Nodal analysis is a method used in electrical circuit theory to determine the voltage at each node, or junction, in a circuit. It involves setting up a system of linear equations based on Kirchhoff's voltage law to solve for the unknown node voltages, allowing for the analysis of complex circuits with multiple branches and power sources.
Norton's Theorem: Norton's Theorem is a method used in electrical engineering to simplify complex electrical circuits by replacing them with an equivalent circuit consisting of a current source and a parallel resistance. This theorem allows for easier analysis and calculation of voltages and currents within the circuit.
Ohm: Ohm is a fundamental unit in electrical engineering that represents the measure of electrical resistance in a circuit. It is a crucial concept that underpins the understanding of Ohm's law and the behavior of parallel circuits.
Ohm's Law: Ohm's law is a fundamental principle in electrical engineering that describes the relationship between the voltage, current, and resistance in an electrical circuit. It states that the current flowing through a conductor is directly proportional to the voltage applied across it, and inversely proportional to the resistance of the circuit.
Parallel Circuit: A parallel circuit is an electrical circuit in which components are connected along multiple paths, allowing current to flow through different branches simultaneously. This type of circuit configuration is characterized by a common voltage across all the components and the ability to add or remove individual components without affecting the operation of the others.
Power Dissipation: Power dissipation refers to the amount of electrical power that is converted into heat energy within an electrical component or circuit. It is the process by which electrical energy is lost as thermal energy, often due to resistance in the system.
Resistor: A resistor is a passive electronic component that is used to control or limit the flow of electric current in a circuit. It is a fundamental building block of electronic circuits, playing a crucial role in various topics, including Ohm's law, series circuits, parallel circuits, and electric power.
Thévenin's Theorem: Thévenin's theorem is a fundamental concept in electrical circuit analysis that simplifies the analysis of complex circuits by replacing them with an equivalent circuit consisting of a voltage source and a series resistor. This theorem allows for the analysis of a circuit's behavior at a specific point or terminal, making it a powerful tool for understanding and designing electrical systems.
Volt: The volt (V) is the unit of electric potential, which is the amount of work required to move an electric charge from one point to another. It is a fundamental unit in the study of electricity and is essential for understanding concepts like electric potential, Ohm's law, and parallel circuits.
Voltage Divider: A voltage divider is a simple circuit that produces an output voltage that is a fraction of its input voltage. It is a fundamental concept in electrical engineering and is widely used in electronic circuits to provide a desired voltage level from a higher source voltage.
Voltage Drop: Voltage drop is the decrease in electrical potential that occurs when current flows through a resistive component, such as a wire, a resistor, or any other electrical device. It is a fundamental concept in understanding the behavior of electrical circuits.
Wattage: Wattage is a measure of the rate of energy transfer or power consumption in an electrical circuit. It represents the amount of work done or energy used per unit of time, and is a fundamental concept in the study of parallel circuits.