Circuits & Networks II: Transients Lecture 1

A sudden change in the state of a circuit, often caused by the opening or closing of a switch, causing the response of the circuit to be highly dependent on time.

The time-invariant element in a circuit that does not store energy but dissipates it as heat.

The time-variant element in a circuit that stores energy in a magnetic field when current flows through it.

The time-variant element in a circuit that stores energy in an electric field when a voltage is applied across it.

The state of an inductor immediately after a switch is closed (at t=0+), where it behaves like an open circuit. This happens because the inductor resists instantaneous changes in current.

The state of an inductor after sufficient time has passed (at t=∞), where it behaves like a short circuit. This is because the current through the inductor stabilizes.

The state of a capacitor immediately after a switch is closed (at t=0+), where it behaves like a short circuit. This happens because the capacitor resists instantaneous changes in voltage.

The state of a capacitor after sufficient time has passed (at t=∞), where it behaves like an open circuit. This is because the voltage across the capacitor stabilizes.

The value of current flowing through an inductor before a switch is operated (at t=0-) which reflects the energy stored in the inductor.

The value of voltage across a capacitor before a switch is operated (at t=0-) which reflects the energy stored in the capacitor

The time constant of an RL circuit, representing the time it takes for the current to reach approximately 63.2% of its final value. It is calculated as τ = L/R.

The time constant of an RC circuit, representing the time it takes for the voltage across the capacitor to reach approximately 63.2% of its final value. It is calculated as τ = RC.

The complete solution for the current in a circuit is the sum of the transient response (ICF) and the steady-state response (IPI).

The part of the current response in a circuit that represents the temporary, time-dependent behavior, often exponentially decaying. It is calculated from the complementary equation of the circuit.

The part of the current response in a circuit that represents the stable, constant behavior after sufficient time has passed. It is calculated based on the steady-state conditions of the circuit.

A type of circuit with a resistor, inductor, and capacitor connected in series. It exhibits a second-order response due to the interaction of these elements.

The discriminant of the characteristic equation of an RLC series circuit, calculated as ∆ = (R/2L)2 - 1/(LC)

A type of response in an RLC circuit where the roots of the characteristic equation are real and distinct (∆ > 0). The circuit returns to its steady state slowly, without any oscillations.

A type of response in an RLC circuit where the roots of the characteristic equation are real and equal (∆ = 0). The circuit returns to its steady state the fastest possible way without any oscillations.

A type of response in an RLC circuit where the roots of the characteristic equation are complex conjugates (∆ < 0). The circuit returns to its steady state with oscillations.

The technique of representing circuit variables like currents and voltages as functions of Laplace variable 's' to solve differential equations.

A mathematical method for decomposing a complex Laplace function into simpler fractions, aiding in the process of finding the inverse Laplace transform.

The process of obtaining a time-domain solution from a Laplace function in the s-domain.

The process of solving a circuit with two switching operations, requiring the analysis of both initial states and steady states.

The initial condition of a circuit, representing the state of an inductor or capacitor before a switching event. It is represented by IL(0) for inductor and VC(0) for capacitor.

The current or voltage values calculated in the circuit before a switching operation, indicating the status of the inductor or capacitor before the change.

The values of current or voltage calculated in the circuit after a switching operation, indicating the transient or steady-state response of the circuit after the change.

The energy stored in an inductor due to its initial current. It is calculated as ½ LI2.

The energy stored in a capacitor due to its initial voltage. It is calculated as ½ CV2.

A technique for analyzing circuits in the s-domain, using Laplace transforms to represent circuit variables and solving equations in the s-domain.

The initial condition of an inductor in the s-domain represented as IL(0)/s.

The initial condition of a capacitor in the s-domain represented as VC(0)/s.