Explore passive elements in electric circuits, including resistors, inductors, and capacitors, their symbols, and units like ohms, henry, and farad, plus the distinction from active elements.

Learn how independent voltage and current sources act as active circuit elements, delivering constant voltage or current while the resulting values adapt to the connected circuit.

Explore dependent sources, including voltage controlled voltage sources and current controlled voltage sources, and how they model transistors and op-amps in ICs.

Calculate the powers absorbed or supplied by circuit elements with independent and dependent sources, as the example confirms 40 W supply equals 16 W, 9 W, and 15 W absorbed.

Apply basic laws to determine voltage, current, and power in dc circuits using Ohm's law, current and voltage laws, voltage divider rule, current divider rule, and delta-store transformation.

Define resistance and its role in a direct-current resistive circuit. Give the formula R = ρL/A and note conductors have low resistivity while insulators have high resistivity, measured in ohms.

Explore Ohm's law, linking voltage, current, and resistance in a resistor with V = I R and I = V / R, and explain how polarity affects power absorption.

Explain short circuit and open circuit with Ohm's law: short circuits have zero resistance and voltage, with any current. Open circuits have infinite resistance and zero current, any voltage.

Define conductance as the reciprocal of resistance, with G in siemens. Compute resistor power via P = VI, P = I^2R, or P = V^2/R, noting it is always positive.

Apply ohm's law to a 30-volt source across a 5 kiloohm resistor to find a current of 6 milliamps, conductance of 2×10^-4 siemens, and power of 0.18 watts.

Define branches as single elements and identify nodes and loops as key circuit concepts, using simple circuit examples. Prepare for Nyquist techniques and Nyquist methods.

Explore loops and meshes in electric circuits, identify independent loops, and apply the fundamental theorem of network topology: branches = nodes + independent loops - 1.

count branches, nodes, and loops in the circuit example, identifying five branches, three nodes, and three independent loops, and apply the equation B = N + L − 1.

Apply Kirchhoff's current law to nodes and closed boundaries, equating currents entering a node to currents leaving it, and treat any closed boundary as a big node for current balance.

Apply Kirchhoff’s voltage law to circuits by summing voltages around a closed loop to zero. Use loop direction, sign conventions for sources and resistors, and the loop equation.

Apply Kirchhoff's voltage and current laws to set up and solve circuit equations for currents. Follow a clear sequence to assign currents, derive equations, and compute voltages and powers.

Apply KVL and KCL to solve a series circuit, determine the current, and compute v1 and v2 across 2 ohm and 3 ohm resistors using Ohm's Law.

Apply kvl and kcl to a circuit, assign currents, form two equations from a loop and a node, then compute currents and the 8 ohm voltage using Ohm's law.

Apply KVL and KCL to a three-current circuit, derive three equations, solve for i1, i2, i3, then compute v1, v2, v3 via Ohm's law.

Apply circuit reduction by identifying series resistors to compute a single equivalent resistance. Sum the resistances of R1 and R2 to obtain this equivalent, enabling simpler circuit analysis.

Explore the voltage divider rule for two resistors in series, deriving V1 = V·R1/(R1+R2) and V2 = V·R2/(R1+R2) to determine each voltage from the total voltage.

Explore parallel resistors and how to find their equivalent resistance. See that they share the same two nodes and voltage, giving 1/R_eq = 1/R1 + 1/R2, for two resistors.

Apply current divider concepts to two parallel resistors, using Ohm's law and the total current to compute I1 and I2 from R1 and R2, and relate to equivalent resistance.

Learn to reduce a seven-resistor circuit to a single equivalent resistance using series and parallel combinations, calculating the overall resistance step by step.

Apply circuit reduction to find the equivalent resistance between A and B by systematically reducing parallel and series resistors, guided by step-by-step examples.

Use current divider for parallel resistors to find branch currents i1 and i2 from the total current, then derive the total current via equivalent resistance.

Identify star and delta configurations to simplify circuits when no resistors are in series or parallel, and learn how resistors form a star with a common point or triangle delta.

Learn delta to star transformation to convert a delta network to a star, derive r1, r2, r3 from the delta values, and apply the equal-resistor special case.

Master star to delta transformation by converting a star resistor set into delta resistors E, B, and C. Use the equal-resistor case to simplify circuits for series and parallel reductions.

Apply store to delta and delta to store transformations to simplify a circuit, compute the total resistance between A and B, and determine the supply current.

Apply Ohm's law and basic circuit reduction techniques to analyze resistors in series and parallel, and compare lighting configurations for reliability and maintenance.

Analyzes a nine-volt lighting system with three bulbs of 15, 10, and 20 watts, calculating total current, individual currents, voltages, and resistances using ohm's law.

Apply nodal analysis to solve circuits by treating node voltages as variables and selecting a reference node. Form and solve current-law equations at non-reference nodes to determine voltages and currents.

apply nodal analysis to determine node voltages in a three-node circuit, set a reference node, write two equations for v1 and v2, and solve with a calculator.

Apply nodal analysis to a circuit with a dependent current source, define node voltages, and solve three equations in three unknowns to find v1, v2, and v3.

Learn how to apply nodal analysis to circuits with voltage sources by using reference and non-reference nodes, forming super nodes, and solving voltages with case one and case two.

Apply nodal analysis with a super node to solve the circuit with 21 V and 9 V sources; determine v1 and v2, then compute V and the 2-ohm current.

Learn the mesh analysis method by modeling circuits with two mesh currents, assuming clockwise directions, and applying Kirchhoff voltage laws to derive two equations and solve the circuit.

Apply mesh analysis to determine the mesh currents i1 and i2 in a circuit, using clockwise directions and Kirchhoff's voltage law to form and solve two equations.

Apply mesh analysis to a circuit with a current-controlled voltage source; derive i1, i2, i3 and obtain i1 = -45/14 A, i2 = -135/14 A, i3 = -5 A.

Master mesh analysis by handling current sources: determine a single-mesh current or form a super mesh when a source lies between two meshes to solve circuits.

Master mesh analysis with current sources in a four-mesh circuit, applying a supermesh to determine i1, i2, i3, i4 and compute x, y, z currents.

Explore the concept of linearity in electric circuits, defining linear elements by homogeneity and additivity, and illustrate with a resistor using Ohm's law, linking to linear circuit theorems.

Identify linear circuits as additive and homogeneous, with output linearly related to input, as in a resistive circuit where halving the input halves the current, while power is nonlinear.

Explore a linear circuit using Ohm's law and a current divider in parallel resistors to find the output voltage across an eight-ohm resistor.

Explore linear circuits through a nodal-analysis example, determining the output node voltage and the source voltage needed to achieve one volt, and applying the linearity property to scale results.

Apply the superposition principle to linear circuits by isolating independent sources and computing each source's contribution to the voltage across the four-ohm resistor. Sum the contributions, keeping dependent sources intact.

Apply superposition to an electric circuit by activating sources individually, using voltage and current dividers to compute output voltage across a resistor.

Apply superposition to a circuit with independent and dependent sources, solving for v0 and the 10-ohm resistor current. Use mesh and nodal analysis to obtain results.

Explore source transformation, a circuit reduction technique that converts a voltage source in series with a resistor to a parallel current source, and vice versa.

Apply source transformation to solve a circuit by converting a current source in parallel with ten ohms to a voltage source in series, then find vx across the eight-ohm resistor.

Apply source transformation to convert voltage sources in series with resistors into current sources in parallel, then combine resistors and sources to achieve single voltage source in series with resistor.

Apply Thevenin's theorem to replace a linear circuit with a Thevenin equivalent: a voltage source in series with a resistor, using open-circuit voltage and resistance to find load current.

Apply Thevenin's theorem to replace the circuit with a Thevenin source and resistance, compute v7, and use a voltage divider to find v0 across the 10 ohm load.

Turn off independent sources and apply a test source between A and B to determine Thevenin resistance with dependent sources; use a 1-volt or 1-ampere source and compute Rth as V over I.

applies Thevenin theory to circuits with dependent and independent sources, deriving V7 and R17 between terminals A and B using open-circuit and mesh analysis.

Explore the maximum power transfer theorem and learn to maximize power to a load by matching the load resistance to the circuit's equivalent resistance. Power delivery peaks when match occurs.

Set the load resistance equal to the circuit's equivalent resistance between terminals a and b (nine ohms) to achieve maximum power, where V7 equals 22 volts.

Explain Norton’s theorem by replacing a linear two-terminal circuit with a current source in parallel with a resistor, and relate it to open-circuit voltage and short-circuit current via source transformation.

Apply Norton theorem to find the short-circuit current between terminals A and B, compute Norton current and resistance via mesh analysis and source transformation, and verify with open-circuit voltage.

Discover how capacitors and inductors store electrical energy as energy storage elements, build a capacitor with two plates and dielectric, and analyze series, parallel connections and the capacitance concept.

Define capacitance as Q over V and explore how plate area, separation, and dielectric constant epsilon dictate a capacitor's ability to store charge.

Explore fixed and variable capacitors, understand parallel plate capacitance C = ε A / D, dielectric types (polyester, ceramic, electrolytic), and observe charging and discharging behaviors.

Explore the voltage-current relationship of a capacitor, deriving i = C dv/dt and v = (1/C) ∫ i dt, and show that the stored energy is 1/2 C v^2.

Apply capacitor equations to find voltage from charge on a 3 μF capacitor and energy stored at 40 V, examine current in a 10 μF capacitor with AC voltage.

Understand capacitors in dc circuits: current is zero for constant voltage, so they act as open circuits, while voltage must be continuous and energy is stored rather than dissipated.

This lecture shows calculating capacitor voltage from a piecewise current using v = (1/C) ∫ i dt, yielding voltages at 2 ms and 5 ms for a 1 mF capacitor.

Demonstrates calculating energy stored in two capacitors within a DC circuit by treating them as open circuits, finding current, determining capacitor voltages, and applying E=1/2 C V^2.

Learn to compute the equivalent capacitance of parallel capacitors, where the same voltage applies and current equals the sum of individual currents, giving C_eq = C1 + C2 + C3.

Compute the equivalent capacitance for series capacitors by summing the reciprocals of their capacitances, since 1/Ceq equals the sum of reciprocals of Ci, and the total voltage is the sum.

Apply equivalent capacitance rules for series and parallel capacitors to solve a step-by-step example, using the series formula (C1*C2)/(C1+C2) and parallel addition to reach the final 40 μF.

Explore how an inductor stores energy in a magnetic field and opposes current changes, with more turns and higher permeability core increasing inductance for dc and ac circuits.

Explore air core, iron core, and variable iron core inductors, including solenoid wound, toroidal, and chip inductors, with microhenry to tens of henry ranges for electronics and power systems.

Examine the relation in an inductor: v = L di/dt, derive current from voltage via integration. Show that the energy stored is 1/2 L i^2 and rises with current.

Explore inductor equations for a 1 mH inductor with a 20 cos 100 t mA current, derive the terminal voltage using v = L di/dt, and compute the energy stored.

The voltage across an inductor is zero with constant current, so in DC it acts as a short circuit; inductors store energy in a magnetic field and have winding resistance.

Analyze a dc circuit with a current source, identify open and short circuit behaviors of capacitor and inductor, then compute inductor current, capacitor voltage, and their energies.

Compute the equivalent inductance for series inductors by summing L1, L2, …; for parallel inductors, use 1/L_eq = 1/L1 + 1/L2 + … with the same voltage across each branch.

This lecture presents a complete three-inductor circuit example, solving i1(t) and i2(t) from initial conditions and deriving total current and voltage using L di/dt and series-parallel inductance.

Compare resistance, capacitor, and inductor by relating voltage and current through ohm's law and v-i relations. Analyze energy storage, DC behavior, and series and parallel equivalents with initial conditions.

Explore the operational amplifier as a versatile circuit building block that performs addition, subtraction, multiplication, division, differentiation, and integration, via its two inputs, one output, and power pins.

Explore the equivalent circuit model of an op amp, including input and output resistances and the voltage controlled voltage source. Understand how negative feedback yields the closed-loop gain.

Examine practical limits of an op amp: output is limited by supply voltages, causing saturation; stay in the linear region where output equals gain times differential input to avoid saturation.

Explore how to solve a circuit with an op-amp's equivalent model using nodal analysis to determine the closed-loop gain and current through the 20 kilo ohm resistor under negative feedback.

The lecture defines the ideal op-amp with infinite open-loop gain, infinite input resistance, and zero output resistance, and highlights two key properties: zero input currents and v1 equals v2.

Explore the ideal operational amplifier in a closed-loop configuration, deriving the output-to-input relationship and current behavior. Compare ideal and practical op-amp results to assess approximation accuracy.

Explore ideal op-amp inverting amplifier configurations that invert and amplify inputs using feedback. Derive closed-loop gain v_o = - (R_f/R_1) v_in with practical examples.

Explore the noninverting amplifier and its voltage follower, where Vo = (1 + Rf/R1) Vin, and see how the buffer isolates stages with infinite input resistance and minimizes loading.

Apply the superposition principle to analyze an op-amp circuit with inverting and non-inverting configurations, calculating the combined output voltage from two inputs.

Discover how a summing amplifier in an op-amp adds multiple input voltages through resistors R1, R2, R3 to produce a weighted, inverted output with RF setting the gains.

Explore how a differential amplifier subtracts v1 from v2 using op-amp with r1–r4 networks. Derive vout = (r2/r1)(v2 − v1) and ensure zero output when v1 = v2 by ratios.

Design a difference amplifier with inputs v1 and v2 to realize vo = 3 v2 − 5 v1, placing v1 at the inverting input and v2 at the non-inverting input.