The Complete Electric Circuits Course

Apply Kirchhoff’s current and voltage laws to form mesh equations, using consistent loop directions, sign conventions, and Ohm’s law to solve for loop currents.

Master Cramer's rule to solve linear systems by computing determinants, using the coefficient matrix, substituting columns, and solving two by two or three by three matrices.

Define the passive sign convention, showing current flows from positive to negative across a voltage drop, and apply it to Kirchhoff's voltage law with worked examples.

Learn series and parallel resistor concepts, including short and open circuits, current and voltage behavior, and calculating equivalent resistance via series addition and reciprocal parallel rules.

Learn to calculate the equivalent resistance by applying series and parallel rules, examining short circuits at R=0 and open circuits at R=∞ through a practical example.

Compare current division and voltage division in circuits with resistors, a current source, and a voltage source; apply parallel-branch and series-voltage formulas to calculate currents.

apply wye-delta transformations to simplify circuits by converting between y and delta networks, identify series and parallel elements, memorize conversion formulas, and compute the equivalent resistance.

Apply nodal analysis with ohm's law to solve for V1 and V2, using ground reference and Kirchhoff current law for consistency.

Master nodal analysis with voltage sources by forming a super node between two nodes, ignoring parallel resistors, applying the node voltage formula, and solving for unknown voltages.

Master nodal analysis by inspection using conductances G = 1/R, forming node equations with diagonal sums and -G between nodes; find V1 and V2 from an independent current source example.

Learn mesh analysis using Kirchhoff's laws and Ohm's law to solve mesh currents, handle current sources, and set clockwise directions for clear equation solving.

Learn to solve circuits with mesh analysis and current sources by forming a supermesh, defining loop currents I1, I2, I3, and solving the resulting equations to find all branch currents.

Learn mesh analysis by inspection to simplify solving larger circuits, using loop resistor sums, diagonal elements, and sign conventions for independent voltage sources, with an example solving for loop currents.

Choose nodal or mesh analysis to minimize equations. Use nodal analysis for circuits with more nodes or super nodes, and mesh analysis for more meshes or super meshes.

Explore the transistor theory, including base-emitter-collector relationships, key voltages like VB = 0.7 V, and current gain concepts. Learn how to use the equivalent network model for nodal analysis.

Explore a transistor example that uses beta relations to relate Ib, Ic, and Ie and solves with mesh analysis rather than nodal analysis, yielding base, collector, and emitter currents.

Apply the superposition principle to circuit analysis by turning off independent sources (voltage sources shorted, current sources opened), computing each contribution, and summing to find Vx.

Learn to transform voltage sources in series with resistors to current sources in parallel, use ohm's law, and solve circuits efficiently with nodal or mesh analysis, including dependent sources.

Learn how to replace any linear two-terminal circuit with a Thevenin equivalent, activate independent sources, use a test source for dependent sources, and compute Vth and Rth.

Apply Thevenin's theorem to an additional example by deactivating independent sources, inserting a test current source between AB, using nodal analysis to find V, and obtain Thevenin resistance.

Apply Thevenin's theorem with nodal analysis to find node voltages A and X. Build two equations from currents, solve for V_A ≈ 46.14 V and X ≈ 107.73 V.

Explore Norton’s theorem by transforming Thevenin equivalents into Norton equivalents using open and short circuits. Learn to compute Norton current and resistance with nodal analysis and circuit simplifications.

Apply the Thevenin equivalent to find R_th and V_th, then show that maximum power occurs when R_load = R_th, with P_max = V_th^2/(4 R_th).

Explain the theory of operational amplifiers and ideal conditions, identify five standard configurations— inverting, noninverting, buffer, summing, and difference— plus nonstandard setups, with test strategies and key formulas.

Identify the op-amp configuration as a difference amplifier and apply the memorized error formula with the given resistors to obtain a 4 millivolts error.

Master capacitor and inductor formulas, including voltage from the integral of current over time and current from the voltage derivative, and learn series and parallel combinations in circuits.

Demonstrates direct current analysis: capacitors open, inductors short; compute energy with E_L = 1/2 L I^2 and E_C = 1/2 C V^2 for a mixed circuit.

Explore phasor representations of a sinusoid in rectangular, polar, and exponential forms, converting time-domain signals to phasors with amplitude seven and phase 45°, and plotting on the complex plane.

Use the Casio fx-991ES PLUS complex mode to perform phasor arithmetic, convert between polar and rectangular forms with amplitude and phase angle, and apply conjugate rules for square roots.

Master solving simultaneous equations, matrices, and complex numbers on the fx-991ES PLUS Casio calculator, converting between rectangular and polar forms to compute roots, conjugates, and angles in complex mode.

Learn how impedance and admittance relate voltage and current, with z = v/i and y = 1/z, and apply r, l, c formulas, j and ω, plus series and parallel.

Apply impedance analysis in a series resistor–inductor circuit to find current and the inductor voltage using phasors, converting v_s(t) to a phasor and using Z = R + jωL.

Determine leading and lagging sinusoids by converting signals to positive cosines using trig identities and expressing them in phasor form. Conclude that V-1 leads by 160 degrees.

Apply sinusoidal source transformation to convert voltage and current sources, solve for x using impedances, and express results in polar or rectangular form.

Master how to determine the sinusoidal Thevenin impedance of a circuit with complex numbers, convert between rectangular and polar forms, and use a test source with nodal analysis.

Explore sinusoidal Thevenin equivalents by defining the AB impedance, calculating V_A with a first-principles nodal approach, and expressing the result in polar form as a magnitude and angle.

Explore integers, natural numbers, and whole numbers; compare their ranges, then identify rational numbers that terminate or recur and irrational numbers like pi.

Understand notation and interval notation, including round vs square brackets for included or excluded values, open and colored circles, and infinity with round brackets; learn union and intersection of sets.

Learn how explicit form differs from implicit form, make y the subject, and apply implicit differentiation with the chain rule to find y dash, highlighting when multiple derivatives arise.

The derivative is the gradient of the tangent to f at x, written f'(x) or dy/dx. A function must be continuous at a to be differentiable there.

Explore the proof that the limit of sin theta over theta as theta approaches zero equals one, using triangle geometry, arc length, and the squeeze theorem.

Proves that limit as theta tends to zero of (cos theta minus one)/theta equals zero, using a (cos theta plus one)/(cos theta plus one) step, for sine and cosine derivatives.

Demonstrates a trigonometric limit proof using a conjugate, showing that as theta approaches zero, (cos theta - 1)/theta tends to zero by applying the sine-over-theta limit and related identities.

Derive the derivative of arcsin x using implicit differentiation and the chain rule to obtain y' = 1 / sqrt(1 - x^2) with x in [-1, 1].

Explore piecewise functions using the absolute value example f(x)=|x+2|. Derive a two-branch graph: x+2 for x >= -2 and -x-2 for x < -2, ensuring all outputs stay nonnegative.

Identify horizontal and vertical asymptotes by limits: as x approaches infinity or minus infinity, y tends to 0 for y = G(x); as x approaches a, f(x) tends to ±∞.

Master solving inequalities by applying rules, factoring polynomials, and analyzing signs of the rational expression (x^2+3x+2)/(x^2+16) to identify zeroes, exclusions, and nonnegative intervals.

Shows that differentiability at a requires continuity at that point, using the limit definition of the derivative and the limit f(x) as x approaches a equals f(a).

Learn how to differentiate the natural logarithm, using y = ln x and e^y = x. Conclude that the derivative of ln(x) is 1/x.

The intermediate value theorem guarantees that a function continuous on [a, b] attains every value between f(a) and f(b) at some c in [a, b].

Explore maximum and minimum values on a function's graph by identifying absolute and local maxima and minima, and determine the global maximum and minimum across the domain.

Explore composite functions by composing f with g (f(g(x))) and applying substitution rules, showing how the domain of f∘g depends on the range of g, which is x ≤ 2.

Discover the conditions for continuity at a point, including f(a) defined, limit exists, and limit equals f(a). Learn about removable, infinite, and jump discontinuities, and continuity from right or left.

Derive the derivative of arctan(x) using the chain rule. Conclude that d/dx arctan(x) = 1/(1+x^2).

Study derivatives and rates of change, including tangent line, gradient, and limit definitions, with a first-principles x^2+3x+2 example.

Derive the derivative of arccos(x) using the chain rule, relate y = arccos(x) to cos y = x, and obtain y' = -1/√(1−x²).

The absolute value measures a number's distance from the origin, yielding nonnegative results. It follows rules such as |a| = |-a| and sqrt(a^2) = |a|, and describes intervals like |x| < a.

Derive the product rule for two functions, showing that d/dx[a(x)b(x)] equals a(x)b'(x) plus b(x)a'(x), and extend to three functions F, G, H.

Derive the quotient rule by differentiating h(x)=f(x)/g(x) and applying the limit as x changes; obtain h'(x) = [g(x) f'(x) - f(x) g'(x)] / [g(x)]^2.

Demonstrates the derivative of sin x from first principles using the limit definition and trig identities to show d/dx sin x = cos x.

Derive the derivative of cos x from first principles by applying the limit to cos(x+h) = cos x cos h - sin x sin h and factoring terms.

Apply the quotient rule to tan x = sin x over cos x, differentiate sine and cosine, and simplify to obtain the derivative as sec^2 x.

Prove the power rule from the limit definition, showing that the derivative of x^n is n x^{n-1}. Apply to positive and negative exponents with examples such as x^{18} and x^{-3}.

Apply the chain rule to a composite function by differentiating the outer function and multiplying by the inner derivative; the video demonstrates this with a square root example.

Explore radian measure by deriving theta as arc length over the radius, linking arc length, radius, and circumference, including the equivalences 360° = 2π radians and 180° = π radians.

Explore the symmetry of functions, including even functions with f(x) = f(-x) and odd functions with f(-x) = -f(x), illustrated by parabola reflection about the y-axis.