Electrical Circuits: Resistors, Inductors, Capacitors

Circuit Elements

• Circuit elements: An element can be completely described based on its voltage vs. relationship.
• Resistor: If the voltage across an element is linearly proportional to the current flowing through it, then the element is called a resistor.
• Resistance: is described as the property of circuit elements which offers opposition to the flow of current, converting electrical energy to heat.
• Unit: Ohm (Ω)

Inductor

• Inductor: If the voltage across an element is directly proportional to the derivative of current with respect to time, then the element is called an inductor.
• Function: An inductor is designed to store energy in the form of its magnetic field.
• Unit: Henry (H)

Capacitor

• Capacitor: If the voltage across an element is directly proportional to the integral of current with respect to time, then the element is called a capacitor.
• Function: A capacitor is designed to store energy in the form of an electric field.
• Unit: Farad (F)

Current

• Current: The rate of flow of electrons or the rate of charge change over time is called current, and its unit is Amperes (A).
• Convention: The direction of current flow is conventionally taken as the direction of positive charge movement.

Voltage

• Voltage: To move an electron from one point to another point in a specific direction, an external force is required, and this external force is the electromotive force (emf) or voltage.
• Unit: Volts (V)

Voltage and Current Source

• Practical vs. Ideal Sources: Practical sources have internal resistance whereas ideal sources don't.
• Importance of internal resistance: It helps protect the voltage source or current source.
• Transformation: A voltage source can be transformed into a current source, and vice-versa.

Kirchhoff's Laws

• Kirchhoff's Current Law (KCL): The algebraic sum of the currents entering a node is zero.
• Kirchhoff's Voltage Law (KVL): The algebraic sum of voltages in a closed loop is zero.

Series and Parallel Combinations

• Series Combination: Resistances are connected end-to-end. Equivalent resistance is the sum of individual resistances.
• Parallel Combination: Resistances are connected across the same two points. Reciprocal of equivalent resistance is the sum of reciprocals of individual resistances.
• Voltage Division Rule: Used to determine the voltage across individual components in a series circuit.
• Current Division Rule: Used to determine the current flowing through individual components in a parallel circuit.

Mesh and Nodal Analysis Techniques

• Mesh Analysis: Used to find the currents in a circuit using different mesh directions.
• Nodal Analysis: Used to find the voltages at different nodes within a circuit.

Network Theorems

• Superposition Theorem: In a linear bilateral network containing more than one independent voltage or current source, the response in any element is the sum of the responses obtained when each independent source is considered one at a time, with all other sources deactivated.
• Thevenin's Theorem: Any linear bilateral network can be replaced by an equivalent circuit consisting of a voltage source in series with a resistance.
• Norton's Theorem: Any linear bilateral network can be replaced by an equivalent circuit consisting of a current source in parallel with a resistance.
• Maximum Power Transfer Theorem: The maximum power is transferred from a circuit to a load when the resistance of the load is equal to the Thevenin resistance of the circuit.