Fundamentals of Electrical Engineering

Apply electrical standards and conventions by using the si base and supplementary units to express circuit quantities, from base units to derived units like hertz, joule, volt, and ohm.

Solve examples on electric charge and current, deriving current from charge over time and integrating to show q equals m t squared with area under the current-time curve.

Learn to work with numbers in all forms, including whole numbers, decimals, fractions, and percentages, apply order of operations and square roots, and compute three-phase line current from apparent power.

Learn to read diagrams by recognizing symbols for resistors, capacitors, inductors, transformers, switches, and meters, identify nodes, and convert pictorial diagrams to schematic diagrams, voltmeters in parallel, ammeters in series.

Explain the fundamental electrical quantities, including electric charge and current, and show how charge is carried by electrons and protons, with Coulomb, volt, and P = V I.

Ohm's law and related formulas link voltage, current, and resistance in dc and ac circuits, and explore conductor cross-sectional area, materials, and temperature effects.

Explore how temperature affects DC cable resistance and derive R_t = R_0(1+α(T−T0)). Use copper data to illustrate positive temperature coefficient and DC vs AC implications.

Learn how to read resistor color codes to determine resistance, tolerances, and temperature coefficient, covering four-, five-, and six-band resistors with practical examples.

Learn to compute electric power from voltage, current, and resistance using p equals v times i and p equals voltage squared over r, and explore energy in kilowatt hours.

Explain how a resistive heater's power varies with supply voltage using p = v^2/r, deriving r from a 3 kw at 220 v rating, and showing higher voltages raise power.

Explore electrical sources, passive and active elements, and independent and dependent sources. Learn how voltage and current relate, and how sources like voltage, current, and their controls drive circuits.

Identify node, loop, and branch concepts in a circuit, count five nodes and eight branches, and apply B = L + N - 1 to find four loops.

Explore series circuits, where elements connect in a single loop to form one current path; observe that current is the same through every component and stops when opened.

Calculate the total resistance in a series circuit by summing each resistor's value, as illustrated by 1, 2, 3, and 4 ohms totaling 10 ohms.

Use ohm's law to compute voltage drops across resistors in a series circuit, and verify the supply equals the sum of drops; measure with a voltmeter and ammeter.

Learn to use the voltage divider in a series circuit to compute the voltage drop across any resistor without knowing the current, via Vn = Rn / Rtotal times Vs.

Learn how series circuits add voltages from aiding sources and subtract opposing ones, determining total voltage when batteries, solar panels, and transformers are connected in series.

Master Kirchhoff's voltage law by assigning current directions and voltage polarities, then write loop equations to determine voltage drops and unknowns in multi-loop circuits.

Apply Kirchhoff's voltage law to a clockwise current loop in a series circuit, compute the current from resistor drops, and find v_ac equals 36 volts.

Calculate total power in a series circuit by summing the power across each resistor, since current is the same but voltages differ, using P_total = I^2(R1+R2+R3+R4) and P_source = VI.

Calculate power dissipated by each resistor in a series circuit with a time-varying source using voltage division; derive p1(t) and p2(t) from v(t) and total resistance.

Derive bulbs' resistances from P = V^2 / R in a series circuit, compute current, and compare power losses to show the 10-watt bulb glows brighter.

Simulate a three-bulb series circuit to compare brightness as voltage changes; higher resistance yields brighter bulbs, with power following current squared times resistance.

Explore how parallel circuits split the total current into branch currents while applying the node rule, where current entering a node equals the sum of currents leaving.

Learn why voltage is equal across all components in parallel circuits, tied to two common points and a shared source, as shown by 220-volt DC lamps.

Learn how to calculate total resistance in parallel power circuits using Ohm's law, including the 1/R_total = 1/R1 + 1/R2 + 1/R3 formula, with examples.

Apply parallel circuit analysis to find branch currents i1, i2, i3 from V battery across R1, R2, R3 and compute the equivalent resistance to obtain the total current.

Determine the unknown resistance in parallel circuits by applying the total resistance formula for two branches and using reciprocal sums for three branches, with practical examples.

Learn how conductance, the inverse of resistance, sums to total conductance and enables I total = V × G total in a 100‑V circuit with 10, 30, and 50 ohms.

Apply current division to determine each branch current in a parallel circuit using total current and branch resistances. Derive the equivalent resistance to analyze the unknown source voltage.

Apply current division in a two-branch parallel circuit to compute branch currents i1 and i2 from branch resistances and total current, with a worked example.

Calculate the current division in a three-branch parallel circuit using conductances, applying the current divider rule with g1=1/2, g2=1/4, g3=1/6 to find I1, I2, I3 from Itotal.

Apply the current divider in terms of conductance to a two-branch parallel circuit with a total current of 20 A to compute I1 and I2.

Calculate power dissipated in each branch of parallel circuits using p = v i = i^2 r = v^2 / r, and sum branch losses for total power.

Compute power losses in parallel resistors R1 and R2 using current division, derive P1 and P2, and show total power equals current squared times the equivalent resistance.

Compute power losses in parallel conductance circuits using P = V^2 G and P = I^2 R, and apply current division to determine branch currents and total losses.

Explore how parallel circuits deliver rated voltage to multiple devices, with examples from home lighting, switches, and receptacles; contrast with series wiring and voltage drops in power systems.

compare brightness of 50 w and 100 w bulbs in parallel and series with a 220 v source, using v^2/r; parallel favors higher power, series favors higher resistance.

Simulate a parallel circuit with three bulbs: 100 w, 50 w, and 30 w. The bulbs have resistances 36, 72, and 121 ohms, and the lowest resistance glows brightest.

Explain open circuit and short circuit concepts, including zero current with open circuit voltage, infinite resistance, and short-circuit current in a photovoltaic module, plus temperature effects on voltage and efficiency.

Explore short circuits in series and parallel circuits, showing how zero resistance, excessive current, and increased power can damage components, and how fuses protect the supply.

Explore series and parallel resistor combinations and determine total resistance, currents, and voltages using Ohm's law and Kirchhoff's laws in a 64-volt circuit.

Explore analysis of series and parallel resistor networks, calculate total and branch currents, and determine voltages across components using equivalent resistance, current division, Ohm's law, and Kirchhoff's rules.

Explore circuits with dependent sources, including current-controlled voltage and current sources, solving with K.B. equations and node analysis to determine voltages across five, three, one, and two ohm resistors.

Calculate the circuit’s equivalent resistance and total current from a 100-volt source, accounting for battery internal resistance, with series and parallel branches, then determine branch currents and directions.

The lecture demonstrates reducing a circuit to a single source and resistance by combining parallel branches and series segments to a 5-ohm equivalent, with a total current of 11 A.

Explain calculating the equivalent resistance for three resistors in parallel, then combine with series branches and a parallel path, and determine the current from 100 volts across 24 ohms.

Compute the total current by reducing the circuit with parallel and series equivalents, then determine the 32-ohm branch current and its power using Ohm's law and loop analysis.

Reduce the circuit to series and parallel equivalent resistances to compute the total current, then find branch currents and the voltage drop across the 20 ohm resistor.

Calculate the voltage across resistor R2 in a two-resistor circuit using the total voltage and the ratio R2/(R1+R2).

Extend analysis from single-node and single-loop circuits to multi-node, multi-loop networks by applying Kirchhoff's current and voltage laws to determine currents and voltages.

Define node voltages with respect to a ground reference and apply Kirchhoff's current law to form nodal equations; solve with conductance matrices and matrix inversion.

Learn to solve a linear system with two variables using matrix form and determinants, applying Cramer's rule to find x and y via delta, delta1, and delta2.

Apply nodal analysis to a two-node circuit, form the node equations for v1 and v2, and solve with a matrix to find v1=1 V and v2=4 V.

Solve a three-node circuit using nodal analysis by formulating two equations for v1 and v2, then solve with matrix determinants to find the node voltages.

Apply nodal analysis to a four-node circuit, writing KCL equations for v1, v2, and v3 with currents leaving or entering, preparing to solve with the kara-murza rule.

Learn to solve a system of three equations in three unknowns using a three by three coefficient matrix, determinants, and Cramer's rule to find x, y, and z.

Apply nodal analysis with conductance to form the circuit equations. Solve via determinant methods and Cramer's rule: v1 ≈ 1.21 V, v2 ≈ 0.80 V, v3 ≈ 0.56 V.

Learn to write node voltage equations quickly using conductances, choose a reference node, and formulate KCL-based equations for multiple nodes, culminating in the matrix form of nodal analysis.

Apply nodal analysis to circuits with independent voltage sources, determine known node voltages va and vb, and solve for v1 and branch currents using conductances.

Apply nodal analysis to circuits with independent voltage sources by forming a super node, writing equations at B and the super node, and solving for Va and Vb.

Apply nodal analysis with a super node created by an independent voltage source; VB − Va = 8 V yields Va = −2.5 V and VB = 5.5 V.

Explore nodal analysis with dependent voltage sources, applying kcl, substituting controlled voltages, and solving the resulting matrix with determinants to find v1, v2, and v3.

Apply nodal analysis to a circuit with a voltage source and derive node equations. Determine v1 and v3 via matrix methods, showing v2 equals v3 and zero current through r3.

Apply nodal analysis to a circuit with a voltage-controlled current source. Relate voltages across parallel 12 ohm and 9 ohm resistors to currents I1 and I2.

Apply nodal analysis to a two-node circuit, solving for v1 and v2 via matrix equations, and find I_x as -5.2 A because the assumed direction is opposite.

master nodal analysis with super nodes and a dependent voltage-controlled voltage source, form and solve node equations with a matrix method to find v1 to v4.

Apply nodal analysis to a two-node circuit using conductances g1–g4, solve for v1 and v2 via a 2x2 matrix, then compute the current and power from the 5 volt source.

Apply nodal analysis to determine node voltages using a super node and kcl, obtaining vb from the independent source and solving for vc, vd, and finally va.

Apply nodal analysis with a super node to solve for v1 and v2, enforcing v2 minus v1 = 2 V and using a matrix approach.

Explore loop analysis with independent voltage sources using Kirchhoff's voltage law in planar circuits, define loop currents, and form equations to determine currents and voltages, contrasting with nodal analysis.

Apply loop equations to a two-loop circuit, form and invert a 2x2 matrix, solve for I1 and I2, and verify with loop equations.

Apply loop analysis to a two-loop circuit, solve for currents i1 and i2 using a matrix approach, then compute power dissipated in branch AB as (i1−i2)^2 times the branch resistance.

Assume three clockwise loop currents I1, I2, and I3 in the circuit. Apply Kirchhoff's voltage law to write loop equations and form a coefficient matrix to solve for the currents.

Apply loop analysis to a three-loop network, form and solve loop equations, and use a 3 by 3 inverse matrix to find i1=6.5 A, i2=6.2 A, i3=-8.8 A.

Use loop analysis on a three-loop circuit, assign currents i1, i2, i3, and solve with a coefficient matrix to obtain i1 1.24 A, i2 0.75 A, i3 1 A.

Apply loop analysis to circuits with independent current sources, determine I1, and solve for I2 using shared resistances and voltage sources V1 and V2 to obtain VB.

Use three-loop Kirchhoff analysis to find loop currents I1, I2, and I3, then compute branch current I2, power from the voltage source, and V_cd via matrix inversion.

Apply loop analysis to compute three mesh currents i1, i2, i3 in a multi-loop circuit using kcl and kvl, including shared current sources and node equations.

Explain the difference between a loop and a mesh, then solve a two-mesh circuit with a shared current source using a super mesh and Kirchhoff's voltage law to find currents.

Apply loop analysis to determine mesh currents in a circuit with a supermesh, then solve for I2 and I3 and analyze voltage drops across 4 ohm and 8 ohm resistors.

Determine mesh currents in a circuit with dependent current source using super mesh and relate vx to i2 and i1 across 200 MΩ, then solve for i1, i2, i3, i4.

Use loop analysis with a super mesh to handle a dependent current source, derive equations, and compute i1 = 5 A and i2 = -5 A.

Learn to write loop equations for resistive circuits with a dependent voltage source using mesh analysis. Solve two equations for i1 and i2, then compute vx across 4000 ohms.

Use mesh analysis to determine loop currents in a circuit with independent current and voltage sources, yielding i1 = 12 a, i2 = 0 a, and va = -48 v.

Apply mesh analysis to determine i1, i2, i3, i4 using two supermeshes and a dependent current source, then compute node voltages via KCL and KVL.

Learn to solve circuits with a dependent current source using mesh analysis with a supermesh and nodal analysis with a supernode. Derive V3 across a 40-ohm resistor, about 104.15 V.

determine node voltages for a nonplanar circuit by nodal analysis, applying kcl and ohm's law, form the conductance matrix, and solve via cramer's rule to obtain v_a, v_b, v_c.

Explore star Y and delta connections, how to connect resistors and motor windings, and how to convert between star and delta to simplify circuit analysis.

Learn delta to star transformation by deriving the equivalent star resistances Ra*, Rb*, Rc* as Ra*=(R1R3)/(R1+R2+R3), Rb*=(R1R2)/(R1+R2+R3), Rc*=(R2R3)/(R1+R2+R3).

Apply delta-to-star transformation to a 4 ohm, 2 ohm, 6 ohm delta network, convert to a star, and compute the circuit's total resistance.

Apply delta-to-star transformation to a 5-ohm, 15-ohm, and 10-ohm delta, compute star resistances, and find a total resistance of 6.66 ohms yielding 1.5 amps at 10 volts.

Apply delta-to-star transformation to convert a delta network to a star network, then compute total resistance by combining parallel and series branches, resulting in two ohms.

Determine the circuit's equivalent resistance by applying delta to star conversions, simplify branches ab and cd in series, then combine parallel branches to obtain a total of 23 ohms.

Apply delta-to-star conversion to simplify a mixed resistor network, combine series and parallel resistances, and determine the total resistance of the circuit (32.35 ohms).

Master star to delta and delta to star transformations, and compute the equivalent resistance between terminals A, B, and C. Derive R1, R2, and R3 from the network equations.

Apply star-to-delta and delta-to-star conversions to a three-resistor network and compute the equivalent resistance between terminals a and b, yielding 4.23 ohms.

Apply star-to-delta transformation on the 4, 8, 15 ohm network to obtain delta resistances r1, r2, r3, then reduce the circuit to calculate the battery current of 2.83 A.

Learn how to convert equal star resistors to delta, find the equivalent delta resistance, and compute the total resistance between terminals a and b using series and parallel steps.

transform a delta of equal resistors to an equivalent star, compute branch resistances, then combine in series and parallel to obtain a total resistance of 10.28 ohms.

Master source transformation between voltage sources with series resistance and current sources in parallel, derive equivalent values, and apply Kirchhoff's voltage law to ensure valid parallel connections.

Demonstrate source transformation by showing resistance in series with a voltage source equals resistance in parallel with a current source, using open-circuit and short-circuit tests and Kirchhoff's law.

Apply source transformation to convert a voltage source with series resistor to a parallel current source and resistor, then compute the 4-ohm and 5-ohm parallel and total current.

Transform the voltage source with zero resistance into an equivalent current source in parallel with a 30 ohm resistor; apply Kirchhoff voltage law to find about 0.22 A.

apply source transformation to convert parallel sources into equivalent voltage sources, perform nodal analysis to find v1 = 7 v, and compute 1.13 a through the 10–ohm and 5–ohm resistors.

Apply source transformation to convert a parallel current source and resistor into an equivalent voltage source with series resistance, then use current division to find the 4 ohm branch current.

Apply source transformation to a circuit with a dependent voltage source controlled by the 50 ohm resistor current. Convert to dependent current source in parallel and determine node two voltage.

Explore the difference between linear and nonlinear circuits, contrasting linear elements that obey Ohm's Law with nonlinear devices like diodes. Explain why the superposition theorem does not apply to power.

Apply the superposition theorem to linear networks, computing currents as the algebraic sum from each independent source while keeping dependent sources active and shorting voltage sources and opening current sources.

Apply the superposition theorem to a circuit with two opposing voltage sources. Compute the equivalent resistance of the parallel pair and determine I total as E1/Req minus E2/Req.

Apply the superposition theorem to determine the current through a 3 ohm resistor by deactivating sources with open and short circuits, using current division and nodal verification.

This lecture applies the superposition theorem to three ohm resistor with 20 volt source and current source, showing nodal analysis yields a different result and power is not linear.

Apply the superposition theorem to find the current through the 12 ohm resistor, using current division and series–parallel reductions, then sum components algebraically.

Apply the superposition theorem to determine current through a one-ohm resistor by activating each independent source, using short/open circuits and current division to sum i1, i2, i3 to four amperes.

Apply the superposition theorem to determine v_ab by activating one source at a time and using open and short circuit substitutions; sum the contributions to obtain 16 volts.

Apply the superposition theorem to determine the current in the six-ohm resistor, using nodal analysis with a dependent current source controlled by that current, activating independent sources.

Apply the superposition theorem to the five ohm resistor: i_x = 3 A from 30 A source, plus i_x = 2 A from the dependent voltage source, totaling 5 A.

Use the superposition theorem to find v_x across 3-ohm resistor in a circuit with three independent sources and a dependent source, open/short deactivations and Kirchhoff voltage law, yielding -8 volt.

Apply the superposition theorem to find the voltage across the 4 ohm resistor by performing loop analysis, solving with matrix methods, and combining source contributions.

Apply Thevenin's theorem to replace any two-terminal linear network with a Thevenin voltage source in series with a Thevenin resistance, computed from open-circuit voltage and deactivated sources.

Apply Thevenin's theorem to determine open-circuit voltage across terminals AB. Then compute Thevenin resistance and load current from a 30 V Thevenin source in series with 7.75 and 12 ohms.

Apply Thevenin's theorem to simulate a circuit with 5-ohm and 12-ohm resistors, yielding a 30 V Thevenin voltage, 7.75-ohm resistance, and 1.52 A in the 12-ohm branch.

Compute the open-circuit voltage and Thevenin resistance for the circuit, then confirm the Thevenin voltage across the 2-ohm load using mesh and nodal analyses.

Apply Thevenin's theorem to find the current in the 10 ohm load by calculating the open-circuit voltage and Thevenin resistance (17 ohms) and deriving 0.37 A.

Apply Thevenin's theorem to determine the current in the 20 ohm load. Compute the open-circuit voltage and Thevenin resistance (63 V, 4.67 ohm) to yield a 2.55 A load current.

Apply Thevenin's theorem to the three-ohm load by computing the open-circuit voltage (38 V) and the equivalent resistance (4 ohms), then determine the current as 38/(4+3) = 5.43 A.

Apply Thevenin's theorem to the circuit to find the current through the 331 ohm resistor by computing the open-circuit voltage, Thevenin resistance, and the load current (1.25 A).

Apply Thevenin's theorem to a circuit example. Disconnect load and solve mesh currents to find v7 and the current through the 1-ohm resistor, and compute the equivalent resistance.

Calculate the open-circuit voltage and mesh currents, then derive the Thevenin equivalent via delta transformation to determine the current through the 3-ohm load.

Apply Thevenin's theorem to circuits with dependent sources by finding Thevenin resistance either via short-circuit current between terminals a and b or via a test source with independent sources off.

Apply Thevenin's theorem to a resistor network: determine the short-circuit current, find the Thevenin resistance, and compute the power loss in the 2-ohm resistor using Thevenin and superposition methods.

Apply Thevenin's theorem to find the current through the 16 ohm resistor by open-circuiting, analyzing the dependent source, then short-circuiting terminals A-B to determine the short-circuit current and Thevenin equivalent.

Apply Norton’s theorem to two-terminal networks. Use a Norton current source in parallel with a Norton resistor; current equals short-circuit current and resistor equals the equivalent resistance with sources off.

Determine the Norton current by shorting the load terminals and using source transformation and current division to find the Norton resistance and load current.

Apply Norton’s theorem to find the short-circuit current and the equivalent resistance, then use current division to find 3.24 A through the one-ohm resistor and compute approximately 10.49 W.

Apply Norton's theorem to determine the load current through the 10-ohm resistor by computing the Norton current from the shorted terminals using a supermesh, then find Norton resistance.

Apply Norton’s theorem to find the short-circuit current and Norton resistance for a 10-ohm load, then compute the load current.

Apply Norton’s theorem to a circuit with a dependent source, using a test source to find i_subtest and v_subtest, obtaining 1 ohm Norton resistance and 10 A current.

Compute the Norton equivalent of the circuit by shorting the load, deriving the open-circuit voltage and short-circuit current, then find the Norton resistance and the current through the one-ohm resistor.

Use Norton theorem to find the short-circuit current (0.2 A) and open-circuit voltage, giving R_N = 6 Ω. Then compute V_L = I_N (R_N || R_L) = 0.3 V.

Apply Norton’s theorem to determine short-circuit and open-circuit voltages, then compute the Norton resistance and the load current; Rn = 0.8 ohm, the load current = 6 A.

Discover the maximum power transfer theorem: maximum load power occurs when the load equals the source's internal resistance, with 50% efficiency; derive Pmax = V^2 / (4 Ri).

Analyze efficiency at maximum power transfer by comparing load power to input power, showing efficiency equals load resistance over total resistance and reaches 50 percent when load equals internal resistance.

Apply the maximum power transfer theorem by removing the load, finding the open-circuit voltage via Thevenin's theorem, and turning off sources to set the load equal to the Thevenin resistance.

Explore the limitations of the maximum power transfer theorem for linear circuits, its inapplicability to bulk power systems, and how reducing losses improves transmission efficiency above 80%.

Simulate the maximum power transfer theorem with a battery and a five-ohm internal resistance. Observe peak load power when the load equals the source resistance, then it drops.

Apply the maximum power transfer theorem, compute 7 Ω plus 5 Ω ∥ 10 Ω total as 10.33 Ω, then set load to 10.33 Ω for about 4.3 W.

Apply nodal analysis to determine the load resistance for maximum power transfer from a 20-volt source, and compute the maximum load power as about 39.3 mW.

determine the load resistance for maximum power transfer in a circuit with a dependent voltage source, a four-ohm resistor, and source transformations, yielding a maximum power of six watts.

Apply Norton theorem to maximize power transfer by calculating the Norton current and Norton resistance, then set the load equal to the Norton resistance.