Circuit Analysis - Complete Course (65+ Hours)

Review charge, electrons, protons, and their role in current and voltage with unitary method and charge conservation, setting the context for network analysis.

Current is the flow of charge over time, expressed as i = dq/dt or i = q/t in amperes. Direction depends on charge carriers and the flow through a conductor.

Understand voltage as work per unit charge in volts, using a reference point for potential difference V12 = V1 − V2 and noting battery versus voltage source.

Compute power as P_t = V_t I_t, with watts as joules per second, and use passive sign convention—consider current direction and voltage polarity to decide absorbed or supplied power.

Explore the concept of energy as power over time. Learn how to calculate energy in joules and watt-hours, and apply energy conservation with VI relationships and circuit elements.

Practice questions on the basics of circuit theory cover power, energy, voltage, charge, and current using unitary methods and time-varying current.

Explore how time-dependent current yields charge via integration from 0 to 5 seconds and how to assess power in circuit elements as absorbed or supplied.

Learn the classifications of sources in circuit analysis, including independent and dependent voltage and current sources, with dc and ac types and their symbols.

Discover how circuit elements are defined by VI characteristics, classify them as active or passive, bilateral or unilateral, lumped or distributed, with examples like resistors, capacitors, inductors, diodes, and sources.

Analyze the VI characteristics to distinguish bilateral and unilateral elements by comparing opposite quadrants, using mirroring across the y- and x-axes to test similarity.

Identify active and passive elements by analyzing VI characteristics and absorbed power, using the sign of P absorbed and the V/I ratio to distinguish active versus passive.

Analyze linearity via homogeneity and additivity to distinguish linear from non-linear elements, with examples y = a x and y = a x + c, and curve y = x^2.

Learn to apply the sub passive sign convention to determine if circuit elements absorb or supply power, using P = VI and energy conservation across example calculations.

Explains charge, current, voltage, power, and energy, and introduces circuit sources, elements, and VI characteristics, plus power calculations and passive sign convention.

Explore resistor fundamentals, including how resistance limits current, Ohm's law, V = IR, passive sign convention, and power dissipation, with short and open circuits.

Explore KCL, KVL, and Ohm's law, using node and loop concepts to solve circuits with algebraic sums equaling zero.

KVL and KCL apply to lumped circuits but not distributed lines; Ohm's law remains valid for both lumped and distributed circuits, yet fails for non-linear elements like diodes.

Identify branches as circuit elements, and nodes as connection points where multiple elements meet. Distinguish paths from loops and apply ohm's law, kcl, and kvl to solve circuits.

Explore basic circuit analysis using KVL, KCL, and Ohm's law through worked examples that calculate currents and voltages in resistors, including dependent sources and passive sign conventions.

Explore how resistors in series share the same current, form an equivalent resistance equal to the sum, and use voltage division to distribute the source voltage.

Master parallel resistances using the current division rule and the condition that parallel elements share the same voltage. Compute individual currents and the equivalent resistance by summing inverse resistances.

Learn to transform practical voltage and current sources with series or parallel resistances to simplify circuits, noting idle sources are not transformable and dependent sources are also applicable.

Explore advanced source transformations for voltage and current sources, apply KVL and KCL to determine equivalent sources, and learn when in-parallel or in-series simplifications are valid or invalid.

Convert delta to star or star to delta to simplify circuits. Apply pi or T formulas to compute RA, RB, RC (or R1, R2, R3) between X, Y, Z.

Solve a 20-volt circuit using KVL, KCL, and Ohm's law to find I1, I2, I3 and V1, V2, V3 in a network with 8, 6, and 3 ohms.

Explore how to solve a simple circuit using multiple approaches: KVL, KCL, Ohm's law, current division, source transformation, and voltage division, to find V0 and branch currents across parallel branches.

Learn to simplify resistor networks to a single equivalent resistance using series-parallel reductions and delta-star conversions.

Explore using equivalent resistance and current division to solve circuits, simplify with series-parallel and star-delta conversions, and apply KVL to find currents and power.

Demonstrates solving circuits with kcl, kvl, and ohm's law to find currents i1, i2, i3 and voltages, paving the way for nodal and mesh analyses.

Master core circuit solving techniques for resistive networks using ohm's law, KCL, and KVL, with series-parallel analysis, current and voltage division, and both source transformations and delta-star conversions.

Introduce nodal and mesh analysis, using KCL and Ohm's law for nodal, KVL and Ohm's law for mesh, to compute node voltages, branch currents, and loop currents in circuits.

Apply nodal analysis using KCL and Ohm's law to determine node voltages v1 and v2, choosing a reference node, assigning branch currents, and solving the resulting equations.

Explore nodal analysis using KCL and Ohm's law to compute node voltages and branch currents across reference and non-reference nodes, with sign conventions and current-source practice.

Explore nodal analysis with voltage sources, including reference vs non-reference nodes, and super nodes formed by two non-reference nodes, plus converting practical sources to current sources.

Identify nodes, form a supernode when a voltage source links non-reference nodes, then apply KCL, Ohm's law, and KVL to find v1, v2, and the current-source voltages.

Apply nodal analysis with a supernode to find v1, v2, and v3 by writing kcl for the normal node and the supernode, using ohm's law and a 22 v source.

Learn nodal analysis for a complex circuit with super nodes, dependent sources, and both KCL and KVL, solving for the four node voltages v1, v2, v3, v4.

practice nodal analysis with multiple circuits, writing kcl equations, applying ohm's law to find node voltages and branch currents, and computing power from a dependent current source.

Explore mesh analysis as a loop-based circuit solving method, distinguish loop, path, and mesh, and learn when to apply KVL, a super mesh, and planar constraints versus nodal analysis.

Apply the mesh analysis procedure to solve circuits by writing kvl equations and using Ohm's law to find loop currents i1 and i2, then compare with nodal analysis.

Apply mesh analysis with kvl to solve for mesh currents i1, i2, and i3, including dependent voltage sources and the super mesh approach.

Learn how to solve circuits with current sources using mesh analysis and the super mesh. Apply kvl, super mesh equations, and source transformation, then compare with nodal analysis.

Master nodal and mesh analysis by recognizing non planar versus planar circuits, choosing based on node-mesh counts, and applying KCL, KVL, and Ohm's law to solve efficiently.

Compare nodal and mesh analysis methods for circuit problems, showing how to set up node voltages and loop currents, apply Kirchhoff's current law and Ohm's law, and choose efficient approach.

compare nodal and mesh analysis for a circuit, showing how to decide the better method and solve for v x, v1, and v2 using kcl, kvl, and source transformations.

Master mesh and nodal analysis to compute node voltages and mesh currents, and choose nodal analysis with a super node or mesh analysis with a super mesh to minimize equations.

Master LTSpice on Windows in a 45+ minute module as part of the circuit analysis complete course.

Learn to install LTspice on Mac, set up a basic circuit, and run DC operating point analysis, including ground, net labels, and viewing node voltages and currents.

Cross-check your node voltages and branch currents by simulating circuits with voltage and current sources, resistors, and dependent sources, using LTspice for DC analysis.

Apply nodal analysis to compute power from a two-volt source in a resistor network. Verify with LTspice using operating point and transient analyses, noting current direction and power delivery.

Explore LTspice setup on Mac and Windows, master basic dc circuit simulations, voltage divisions, nodal analysis, and transient, operating point, and ac frequency responses.

Learn inductors in detail, including energy storage in flux, the relation phi = L i, and v = L di/dt, plus how to compute current from voltage and initial conditions.

Identify key inductor properties: voltage is zero with constant current, and inductors act as a dc short; current cannot change instantly. Compare ideal and practical inductors and their energy behavior.

Explore inductor basics with practical examples: compute voltage from current using v = L di/dt, energy from i via ½ L i², and how initial conditions shape results.

Demonstrates inductor basics with solved examples: calculate current and energy at t=1 s for a 2 H inductor with 0.3 A initial current; analyze energy storage and steady-state behavior.

Analyze series and parallel inductors, apply KVL and KCL to find the equivalent inductance, with example problems and ladder network questions.

Explore voltage and current division in inductors. Analyze series and parallel configurations to derive formulas for v1, v2, i1, i2, and to compute equivalent inductance and energy storage.

Apply series-parallel analysis, KCL, and KVL to calculate initial currents and voltages in a circuit with 4 H, 12 H, and 2 H inductors, yielding I1, I2, V1, and V2.

Explore capacitors as energy storing devices that hold energy in an electric field, and master Q equals C V and I equals C dV/dt.

Explore the properties of capacitors, including I = C dv/dt, why zero dv/dt yields zero current and dc as an open circuit, and ideal vs practical leakage and energy storage.

Explore single capacitor analysis with practical questions on current from voltage via I = C dv/dt and energy stored and voltage under different waveforms.

Explore how a capacitor stores and releases energy under a decaying voltage using the energy formula and series-parallel capacitance to find equivalent values.

Explore circuits composed entirely of capacitors with a dc source, applying series and parallel rules and q=cv to find equivalent capacitance, total charge, and voltages across each capacitor.

Explore circuit theorems from a dc perspective, including superposition, Thevenin's theorem, and Norton's theorem, and learn how delta-wye conversion and source transformation simplify analysis of rl, rc, and rlc circuits.

Apply the superposition theorem to analyze linear circuits with multiple sources. Calculate the voltage or current from each source acting alone, then sum algebraically; power is not linear.

Explore the superposition theorem through diverse circuit examples, applying voltage division, current division, and nodal/mesh analyses to compute V0 and I0 with independent and dependent sources.

This lecture highlights drawbacks of the superposition theorem: heavy work with multiple sources and nonlinearity of power, then shows solving via voltages and currents using P=V^2/R to find max power.

Derive a Thevenin equivalent for a linear two-terminal circuit by replacing the fixed part with a Thevenin voltage source in series with Thevenin resistance, to analyze varying loads and currents.

Apply Thevenin's theorem to complex circuits using nodal, mesh, and source transformation methods to compute vth, rth, and load current, including dependent sources and supernodes.

Explore Thevenin's theorem with dependent sources by calculating v_th and r_th, using supermesh, nodal analysis, and case studies to illustrate circuits with dependent sources.

Explore Norton's theorem, compute the short-circuit current between terminals, and represent the network as a current source in parallel with r_n, with Thevenin equivalents as needed.

Explore Norton theorem through circuit analysis, deriving i_n and r_n from short-circuit and open-circuit conditions, and using nodal analysis. Relate to Vth, dependent sources, and simplifying techniques for easier equivalents.

Analyze Norton and Thevenin behavior for circuits with only dependent sources, showing zero open-circuit voltage, zero short-circuit current, and a negative equivalent resistance.

Apply the maximum power transfer theorem by converting the circuit to its Thevenin equivalent and varying RL to match RL with Rth, maximizing load power.

Explore maximum power transfer in circuits by finding Thevenin voltage and resistance, applying the maximum power transfer condition with varying load, and handling dependent sources.

Apply Tellegen's theorem to verify energy conservation by equating total delivered and absorbed power in a network, using KCL and KVL to determine voltages and currents.

Millman's theorem converts parallel voltage sources with resistances into a single source and resistance, illustrating Vth, Rth, and current calculations for a 5 ohm resistor.

Learn the compensation theorem in circuit analysis: turn off independent sources, insert a series voltage source of I del R at the change, and determine the current change.

Explore reciprocity theorem in linear, passive, time-invariant bilateral circuits; verify that a voltage at one point yields the same current at the other, preserving the response-to-excitation ratio.

Explore advanced circuit theorems to simplify dc and ac analysis, including Thevenin's, Norton's, Millman's, maximum power transfer, reciprocity, delta-star, and source transformation, with guidance on dependent sources.

Examine source-free RC circuits as first-order systems, showing how an initially charged capacitor discharges through a resistor with a natural response v(t)=V0 e^{-t/RC} and time constant tau=RC.

Explore source-free rc circuit examples by converting to Thevenin's equivalent, computing the time constant, and using voltage division to determine vc(t), vx(t), and ix(t) for t>0.

Analyze source-free rc circuits with a switch, covering charging before opening and discharging after, determine the initial capacitor voltage via voltage division and the energy stored and time constant.

Explore the source-free RL circuit, where the inductor current decays as I(t)=I0 e^{-Rt/L} with time constant tau=L/R, linking initial energy to resistor dissipation and voltage relations.

Study source-free rl circuits through simple and dependent-source examples, mastering initial current, time constant, and the i_L(t) = i0 e^{-t/τ} response, including switch-based charging and discharging.

Explore source-free rl circuits with switches, determine the initial inductor current at t<0 and its evolution after switching at t≥0, using the time constant tau = L/R.

Learn how unit step, impulse, and ramp functions model switching in circuits, including their delayed and advanced forms, and their interrelations via differentiation and integration.

Learn to draw and analyze voltage pulses using unit step, impulse and ramp functions by building a five-volt pulse between t=2 and t=5, deriving and sketching its derivative.

Learn to represent waveforms with switching functions by constructing ramps from slopes and unit steps, including zero-start and nonzero-start cases, and apply to RC and RL circuits with sources.

Learn a shortcut for obtaining the RC circuit step response by applying the first-order equation directly to current and voltage under a step input, without always computing the capacitor voltage.

Explore charging and discharging of a capacitor in rc circuits after switching, using a step-response equation for vc(t). Compute v infinity and tau, linking voltages via switching and Kvl.

Explore how multiple switches affect inductor current in RL and RC circuits, derive time constants, initial and final currents, and analyze stepwise examples.

Analyze capacitor voltage in a two-switch rc circuit, showing how it evolves over time as S1 and S2 switch at 0 and 10 ms, using source transformation and time constants.

Learn to verify circuit theory by simulating a discharging capacitor and a source-free rl circuit in LTspice, using initial conditions, node voltages, and transient analysis to match analytical results.

Examine a with-source RC circuit, capacitor voltage 15 V initial and 9.375 V final with a 5.625 e^{-2t} term, validated by LTspice. Then analyze a with-source RL circuit with i(t)=2+3e^{-15t}.

Explore first-order RC and RL circuits, including source-free and switch configurations, analyze charging and discharging dynamics, and relate theory to LTspice simulations.

Study second order circuits by analyzing series and parallel RLC networks, with and without source, and solving their second order differential equations and transient responses through simulations.

Compute initial and final values for an RLC circuit, including i0, v0, i∞, v∞, and the derivatives di0/dt and dv0/dt at t=0+, using kvl and kcl.

examine how to determine initial and final values in rlc circuits by applying kcl, kvl, and current division to compute vr, vl, vc, and il at 0−, 0+, and ∞.

Develop skills to calculate initial and final values of capacitor voltage, inductor current, and resistor voltage in RC and RL circuits using kvl and current division.

Analyze a source-free series rlc circuit using initial values I0 and V0, derive the second-order differential equation, and discuss overdamped, critically damped, and underdamped responses.

Compute alpha and omega naught for a source-free series RLC, identify underdamped natural response, and determine S1, S2 roots and initial conditions to analyze current and capacitor voltage.

Analyze a source-free series RLC circuit with a 0.02 F capacitor, 9 ohms, and 0.5 H inductor under five seconds of transient analysis, noting underdamped, overdamped, and critical damping behavior.

Explore a source-free series RLC example and determine the underdamped current response using alpha, omega_naught, and omega_d. Compute the initial condition constants B1 and B2 from the circuit’s starting values.

Derive the node voltage in the source-free parallel RLC circuit and its second-order differential equation, highlighting alpha and omega_naught and the underdamped, critically damped, and overdamped responses.

Explore a source-free parallel RLC circuit, determine initial inductor current and capacitor voltage, compute alpha and omega naught, identify overdamped response, and derive v t using initial conditions.

Analyze a source-driven series RLC circuit with initial inductor current I0 and capacitor voltage V0. Derive the transient and steady-state responses using KVL, and determine capacitor voltage and inductor current.

Analyze the transient and steady-state voltage across a 10-ohm resistor in a source-driven series RLC circuit, with a switch at t=0 and initial conditions, using a VR expression.

Analyze a source parallel RLC circuit with a six amp current source, finding v_naught for t>0 via transient and steady-state analysis with a critical-type response.

Explore simulations of parallel and series RLC circuits with sources, analyzing inductor current, resistor current, and capacitor voltage under various damping regimes during a 10 s transient.

Analyze the step response of general second-order circuits by formulating the differential equation and using KVL and KCL. Identify initial conditions and distinguish transient from steady-state, noting damping type.

Analyze a general second order RLC circuit to determine capacitor voltage v(t) and inductor current i(t) after the switch closes, revealing an overdamped transient with v∞=20 V and i∞=5 A.

Explore the basics of sinusoids and phasors for AC analysis, converting sinusoidal signals into phasors to apply circuit theory, including frequency and phase concepts.

Learn basic trigonometric identities for sinusoids, convert between cos and sin with phase shifts, and visualize phase differences using phasor diagrams.

Master phasors, a complex-number representation of sinusoids, using rectangular and polar forms to simplify calculations, convert, and relate dv/dt to j omega V.

Master phasor methods by converting between rectangular and polar forms and performing additions, subtractions, and conjugate operations. Convert sinusoidal signals to phasors and apply these tools to solve circuit problems.

Represent resistor, inductor, and capacitor in the phasor domain, relating voltage and current through phasors and impedances jωL and 1/(jωC) for AC analysis.

Apply phasor analysis to find currents in capacitors and inductors for sinusoidal signals, converting time-domain voltages to phasor form and back via Ohm's law.

Learn to model AC circuits with impedances and admittances, convert to phasors, apply series and parallel combinations, and perform steady-state analysis using phasors to find currents and voltages.

Learn to convert between polar and rectangular forms of complex numbers using a calculator, including entering complex mode, computing magnitude and angle, and performing phasor calculations.

Explore the basics of sinusoidal signals and phasor representation, and apply phasors to R, L, and C circuits for steady-state AC analysis.