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RL Circuits
An RL circuit consists of a resistor and an inductor and may have a source of emf connected to it. The inductor in the circuit helps to prevent rapid changes in current, which can be helpful if a steady current is required but the external source has a fluctuating emf. Consider an open RL circuit connected to a source of constant emf. As soon as the circuit is closed, the current begins to increase at a rate that depends only on the value of the inductance in the circuit. The greater the...
LC Circuits
An LC circuit consists of an inductor and a capacitor, either in series or parallel. Consider a charged capacitor connected with an inductor in series. Before the switch is closed, all the energy of the circuit is stored in the electric field of the capacitor. When the switch is closed, the capacitor begins to discharge, producing a current in the circuit. The current, in turn, creates a magnetic field in the inductor. Because of the induced emf in the inductor, the current cannot change...
Circuit Terminology
An electrical network is a system composed of interconnected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, an electrical network does not necessarily form a closed path. In other words, while all circuits can be considered networks due to their interconnected nature, not every network qualifies as a circuit.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
A circuit, on the other hand, is also an interconnected system of electrical elements but must contain one or more closed paths.
RL Circuit without Source
When a DC source is suddenly disconnected from an RL (Resistor-Inductor) circuit, the circuit becomes source-free. Assuming the inductor has an initial current denoted as I0, the initial energy stored in the inductor can be determined.
Applying Kirchhoff's voltage law around the loop of the circuit and substituting the voltages across the inductor and resistor yields a first-order differential equation. A logarithmic equation is obtained by rearranging the terms in this equation, integrating...
Applying Kirchhoff's voltage law around the loop of the circuit and substituting the voltages across the inductor and resistor yields a first-order differential equation. A logarithmic equation is obtained by rearranging the terms in this equation, integrating...
Series R—L Circuit Transients
In a series resistor-inductor (R-L) circuit, closing the switch at the start of the time period simulates a three-phase short circuit, a fault condition where all three phases of an unloaded synchronous machine are short-circuited. When there is no fault impedance and no initial current, the initial voltage is determined by the phase angle of the source voltage.
Using Kirchhoff's Voltage Law (KVL) to analyze this circuit helps determine the total asymmetrical fault current, which consists of...
Using Kirchhoff's Voltage Law (KVL) to analyze this circuit helps determine the total asymmetrical fault current, which consists of...
Boundary Conditions: Lossless Lines
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
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