Electric Circuit analysis:Electronics,Electrical Engineering

Identify linear and nonlinear circuit elements using homogeneity and the superposition principle; recognize linear elements like inductors, resistors, and transformers, while diodes and most semiconductor devices are nonlinear.

The lecture contrasts active and passive elements, showing that active elements require biasing and can amplify signals by drawing power from the bias supply, while passive elements cannot.

Examine time variant elements whose parameters change with time and show aging effects, and compare them to time invariant inductance and capacitance analyzed at a specific instant.

Identify bilateral elements, independent of current direction, such as inductors and capacitors, and unilateral elements like diodes that conduct in one direction with a 0.7 volt forward drop.

Defines resistance as the inherent property opposing current, models a linear, time-invariant relation between input and current, and explains how power becomes heat in a load and in transmission losses.

Inductance resists changes in current by linking flux phi to current and storing energy ½ L I²; practical inductors have resistance and power system applications like filters and current limiting.

Analyze current through an imperfect inductor with series resistance; compute energy dissipated in the resistor and energy stored in the inductor from the area under the power curve.

Explore capacitance as a property storing energy in a capacitor, linking charge, current, and voltage, and examine dielectric loss and practical capacitor models.

Understand how transformers step up or step down alternating current using turns ratio, keep frequency constant, and balance voltage and current while preserving power, not amplifying input power.

learn how to power circuit elements with independent and dependent sources, including practical vs ideal sources, and how voltage or current control defines dependent source types.

Understand independent voltage sources that maintain a constant potential difference across two terminals. Learn about dependent voltage sources whose voltage depends on circuit parameters such as current or another voltage.

Independent current sources set current with a direction and do not depend on circuit parameters; dependent sources are represented by a diamond box and controlled by voltage or current.

Kirchoff's current law states that the sum of currents at a node equals zero, with entering currents negative and leaving currents positive.

Apply Kirchhoff's current law and passive sign convention to circuit segment, using iC = C dv/dt and vL = L di/dt to find currents and voltages in resistor, capacitor, inductor.

Kirchhoff's voltage law states the sum of voltage drops in a closed loop equals zero, with v = iR, v_L = L di/dt, and v_C = (1/C) ∫ i dt.

Learn nodal analysis for electric circuits by identifying nodes, assigning a ground reference, applying Kirchhoff's current law, and forming node equations to solve currents and voltages.

Analyze a circuit to determine loop and branch currents, establish a ground reference, and compute voltages at vab and other nodes.

learn mesh analysis by identifying meshes, assigning mesh currents, applying kvl, solving for currents, and determining power absorbed or delivered by sources.

This example applies Kirchhoff’s laws to a multi-branch circuit, assigns polarities, and solves loop equations to determine currents I and voltages E.

Apply loop analysis and polarity conventions to determine branch currents and solve for the unknown current.

Series connection occurs when exactly two elements share a single node and the currents are equal; inductors add L1+L2, capacitors add 1/(sC1)+1/(sC2), and two current sources cannot be in series.

Two bulbs, 40 w and 60 w, are connected in series; since the 40 w bulb has higher resistance, it dissipates more power and glows brighter.

Analyze a star network with open branches between terminals a–b, b–c, and c–d, and solve three equations for rb and rc to determine resistance values in ohms.

Understand how parallel connections share voltage and divide current, and apply rules for equivalent impedance, capacitor and inductor values, plus why current sources may be paralleled while voltage sources cannot.

Identify parallel and series resistor groups in the circuit, apply the equal-magnitude shortcut in parallel to find half of each resistance, and compute the total current through the network.

Identify directly connected nodes and treat them as a single node to simplify the circuit. Treat parallel capacitors as additive and use 1/(1/C1+1/C2) for the series equivalent.

Remove sources by shorting voltage sources and opening current sources, identify nodes A, B, and C, then simplify resistors in parallel and in series to find the equivalent resistance.

Remove the current source to open the circuit, neglect the unused branch, then combine series resistances to 3 and 7 ohms and find the parallel result of 2.1 ohms.

Explore the voltage division rule in series circuits, showing how the source voltage splits among resistors, inductors, and capacitors according to impedance, with capacitors following the opposite rule.

Apply the current division rule for parallel impedances to find branch currents, using i1 = itot*z2/(z1+z2) and i2 = itot*z1/(z1+z2). Note capacitors oppose this due to inverse impedance.

Analyze a two-branch circuit using current division and a loop rule to determine branch currents, given a total current of eight amps and equal branches.

Explore delta to star and star to delta transformations, derive Z1, Z2, Z3 from delta, and apply equal-impedance cases where delta equals three times the star value.

Convert a delta circuit to a star network by calculating each star leg between a node and neutral using Rab, Rbc, and Rca divided by their sum.

Analyze balance in electric circuits and simplify networks using delta-wye transformation: check balance with opposite-branch products, remove balanced resistors, then convert a delta to a star and compute equivalent resistance.

Learn how to perform voltage-to-current source transformations by converting voltage sources with series resistance into current sources with parallel resistance, then analyze current distribution using current division.

Transform a current source in parallel with a resistor into an equivalent voltage source in series with that resistor. Apply polarity and Kirchhoff's voltage law to solve the single-loop circuit.

Open circuit has no closed path, so current is zero. A short circuit directly connects terminals, creating a low-resistance path that directs current through the short.

Analyze a circuit, and show that in a balanced bridge the current in the targeted branch is zero and the two terminals share the same potential.

Apply the superposition theorem to linear networks by summing responses from each independent source, while leaving dependent sources untouched. The homogeneity principle explains that scaling the input scales the output.

Use superposition to analyze the circuit by open-circuiting the current source and shorting the water source, then apply parallel current division and balance to see zero branch current.

Apply Thevenin and Norton theorems to simplify circuits, transforming networks to a voltage source in series with resistance or a current source in parallel, using open or short circuit concepts.

Use Norden's totem to determine the short-circuit current in the branch, then convert the network into an equivalent current source in parallel with resistance and compute the branch current.

Compute branch current by applying Norton’s theorem with dependent sources, determine open-circuit and short-circuit currents, convert to Norton equivalent, and use current division to find Iex.

Maximize power delivery by applying the maximum power transfer theorem with a Thevenin equivalent circuit. Achieve maximum load power when load resistance equals source resistance, yielding 50% efficiency.

The example shows maximizing power transfer by calculating the Thevenin resistance as 50/21 ohms and setting the load to match it for a maximum power of 8/21 watts.

Tellegen's theorem states that the sum of branch voltages times currents equals zero, reflecting conservation of energy as sources deliver power and loads absorb it.

Determine the voltage across the current source from the node voltages, multiply by the current to get the power, and conclude the current source delivers 3 W.

Study how networks respond over time in the time domain, highlighting transient versus steady-state behavior of capacitors and inductors, and explain amplitude and phase in frequency-domain analysis.

Explore time-domain analysis by distinguishing transient responses from steady-state behavior, driven by energy storage elements, and learn how transient speed and steady-state accuracy shape circuit readings.

Explore how state variables tied to storage elements like inductors and capacitors determine a system’s behavior, including force and natural (zero-input) responses, and initial and final (steady-state) conditions.

Determine circuit order by the highest derivative in the differential equation or the highest s power in the transfer function. First-order systems have one energy storage element; second-order have two.

Analyze a source-free RC circuit, a first-order system where a charged capacitor discharges through a resistor, dissipating energy as heat with voltage and current decaying exponentially with RC time constant.

Explore source-free RL circuits in time-domain analysis, where an initial inductor current causes exponential decay with time constant tau = L/R; analyze current, voltages, energy, and settling time.

Find the RC time constant by removing sources, shorting the voltage source, opening the current source, and computing the equivalent resistance across the capacitor, then multiply by capacitance.

analyze a current source circuit to find its time constant by transitioning from forced to free response, using steady state and a series capacitor equivalent, yielding tau around 6 microseconds.

Find the time constant for the shown circuit with an inductor after shorting the voltage source by computing the equivalent resistance; the result is 1 ms.

Calculate the time constant by simplifying parallel inductors to 7 mH, shorting the voltage source, and combining resistors to find the across-terminal resistance, yielding a 1 ms time constant.

Explore a second order circuit with two inductors that cannot be combined, requiring two state variables (inductor currents) and no unique time constant; use differential equations and characteristic roots.

Explore forced response in electrical circuits by analyzing step inputs and impulse functions, understanding step response of first-order RC and RL networks, and modeling initial conditions.

Analyze the step response of an RC circuit driven by a DC source, deriving the capacitor voltage Vc(t) with RC time constant and distinguishing transient and steady-state behavior.