Ultimate Electrical Circuits for Electrical Engineering

Understand resistance and resistivity, and how length, area, and material determine circuit resistance. The lesson introduces Ohm's law and basic series and parallel concepts.

Explore Ohm's law and the relationship between voltage, current, and resistance, including open and short circuits, fixed and variable resistors, and conductance as the inverse of resistance.

Explore solved examples using Ohm's law to calculate resistance, current, conductance, and power in dc circuits, and introduce instantaneous power in an ac resistor with sine wave input.

Explore branch, node, and loop concepts, apply Kirchhoff's voltage and current laws, and distinguish series versus parallel connections with their currents and voltages.

Learn Kirchhoff's current law and Kirchhoff's voltage law, based on charge conservation and the sum of voltages around a loop; apply these laws using node and loop concepts.

Work through solved examples applying ohm's law, KCL, and KVL to determine node voltages and currents in resistor networks featuring 2-ohm, 3-ohm, and 6-ohm resistors.

Explore voltage division in series resistors and current division in parallel paths; derive equivalent resistances and the conductance analogy, and examine open and short circuits.

Explore solving circuits by finding equivalent resistances through series and parallel combinations, using ohms and step-by-step reductions to replace networks with a single resistor.

Explore delta-wye (delta-star) transformations to simplify non-series, non-parallel resistor networks, converting delta to Y and Y to delta to analyze circuits.

Learn to apply delta-to-Y transformations to convert delta networks into equivalent Y networks, calculate the resulting resistances, and simplify circuits to determine equivalent resistance and current.

Represent devices as resistors to model energy conversion and loads, including wires, bulbs, heaters, motors (with inductance), and home outlets, using parallel and series circuits to analyze current and power.

Master nodal and mesh analysis to solve linear circuits using node voltages, KCL, and Ohm's law, including nodal analysis with no voltage sources and reference ground.

Derive node voltages V1 and V2 for a current source circuit by assuming currents leaving nodes, applying Kirchhoff's current law and Ohm's law, and solving by substitution or matrix method.

Learn to perform nodal analysis with voltage sources, handling cases between reference and non-reference nodes and between two non-reference nodes using super nodes, KCL, and KVL.

Explore nodal analysis with voltage sources, deriving node voltages v1 and v2 through a super node, KCL, and a matrix method illustrated by delta values.

Master mesh analysis without a current source by using loop currents to form a reduced set of equations and apply Kirchhoff's voltage law for each loop.

Apply mesh analysis to circuits with current sources, form loop equations with KVL, and solve via the Kramer method to determine loop and branch currents.

Apply mesh analysis with current sources: treat a single-mesh source as the loop current (negative sign); when the source sits between two meshes, form a super mesh and solve.

Demonstrate mesh analysis with a current source, form loop and supermesh equations, and determine currents, revealing a -7.5 A result indicating opposite direction.

This lesson contrasts nodal and mesh analysis, guiding you to choose the method with fewer equations: mesh for planar circuits with series elements, nodal for parallel elements and non-planar networks.

Analyze a DC transistor circuit using mesh analysis to determine base, collector, and emitter currents and the output voltage, illustrating transistor switching and amplification in power electronics.

Discover circuit analysis of complex circuits using the superposition, source transformation, the seven theorem, and Norton’s theorem to simplify large circuits.

Apply the superposition theorem in linear circuits by analyzing each independent source separately, deactivating others, and summing their voltage or current contributions to obtain the final value.

Apply the superposition theorem to a two-source circuit, deactivate each source to find V1 and V2, and sum them to obtain the total voltage, using voltage and current division.

Apply the superposition theorem to determine circuit currents by deactivating independent sources and using mesh analysis, while noting when a dependent source remains active.

Apply the source transformation theorem to convert a voltage source in series with a resistor to a current source in parallel with a resistor, for independent and dependent sources.

Apply the source transformation theorem to convert a voltage source with series resistance into a current source, then simplify the circuit and compute the 8-ohm voltage using multiple methods.

Apply the source transformation theorem to convert between current and voltage sources in a circuit, analyze v_x across a 4 ohm resistor, and solve for current and voltages.

Learn Thevenin theorem by replacing a linear two-terminal circuit with a single voltage source v seven in series with r seven. Open-circuit voltage and input resistance determine the model.

this lecture demonstrates using Thevenin to replace the circuit with a 30-volt source and 4-ohm R, enabling quick current calculations through the load for RL = 6, 16, 36 ohms.

This lecture applies the Thevenin theorem to a circuit example, using mesh analysis after deactivating independent sources, to find v7 open-circuit as 20 V and Thevenin resistance as six ohms.

Apply Norton theorem to convert a linear two-terminal circuit into a current source in parallel with a resistor, using open-circuit voltage and short-circuit current to determine i_n and r_n.

Demonstrates Norton conversion: compute R_N = 5 Ω || 20 Ω = 4 Ω and I_N = 1 A, producing a 1 A source in parallel with 4 Ω.

Apply Norton theorem to a dependent-source circuit, deactivate the independent source, and determine the short-circuit current and Norton resistance. The result: 7 A Norton current and 5 Ω resistance.

Learn how to maximize power transfer by matching the load resistance to the source resistance. Set RL = R7 to achieve maximum power, with Pmax = V7^2/(4R7).

Determine r_l for maximum power transfer by deactivating independent sources and finding a seven ohm load, using the open-circuit voltage of 22 volts to arrive at 13.44 watts.

Explore how operational amplifiers perform mathematical operations, including addition, subtraction, multiplication, division, differentiation, and integration, by connecting resistors and capacitors. Understand inverting and non-inverting inputs and the power supply.

Explore non-ideal op amp behavior with a detailed example, analyzing input and output resistances, overload gain, and finite gain via KCL, then compare to ideal op amp assumptions.

Explore the construction of ideal operational amplifiers, highlighting infinite gain, infinite input resistance, zero output resistance, with v1 equals v2 and differential voltage vd equals 0.

This lecture compares ideal and non-ideal op amps using a 741 with 10k and 20k resistors, showing v1 = v2 = 0 and vout ≈ -4 V (gain ≈ -2).

Master the inverting amplifier, which inverts the input voltage and multiplies it by a gain of Rf over R1, with the non-inverting input grounded and feedback between output and input.

Analyze an inverting amplifier with input 0.5 V, input resistor 10 kΩ, and feedback resistor 25 kΩ; output is -1.25 V with 50 μA flowing through the 10 kΩ resistor.

Analyze an inverting amplifier circuit by applying kcl with va and vb both 2 v to yield vout of -6 v.

Explore how a non inverting op amp uses feedback to yield vout = (1 + rf/r1) vin, and learn about the voltage follower with unity gain and high input impedance.

Explore a circuit that combines non inverting and inverting amplifiers and solves vout via superposition, yielding an overall -1 volt.

Explore summing operational amplifiers, an inverting amplifier with multiple inputs that produce a weighted, inverted sum of v1, v2, and v3 via r1, r2, r3, and rf.

Demonstrates a two-input summing amplifier, deriving the output voltage and current from v1, v2, and resistors, with vout = -Rf/R1 v1 - Rf/R2 v2 and iout calculations.

This lecture introduces the difference amplifier, which outputs the difference between two inputs amplified by a gain set by four resistors, and rejects common-mode signals.

Design a difference amplifier that yields vout = -5 v1 + 3 v2 using resistor ratios; set R2 = 5 R1 and R3 = R4, with example values.

Explain cascaded operational amplifiers, where input v1 flows through stages with gains a1, a2, and a3 to produce a final output. Emphasize open cascaded configuration and the total gain.

demonstrate cascaded op-amp circuitry with two non-inverting stages and feedback, yielding 150 mV output from 20 mV input, and show iout computed via (vout - vb)/10k.

Explore how an operational amplifier constructs a digital to analog converter using a binary weighted ladder and a summing inverting amplifier to translate binary input into an analog voltage.

Demonstrate a digital-to-analog converter using an op-amp summing inverting amplifier, with a feedback of 80k and 10k input resistors to convert four binary inputs into an analog output.

Explore instrumentation amplifiers, emphasizing differential input amplification controlled by an external gain resistor, enabling precision measurements and applications in isolation, thermocouple, and data acquisition systems.

demonstrates how an instrumentation amplifier amplifies a small voltage difference between V2 and V1 using RG and resistor values to set gain, producing a larger output voltage.

Introduces capacitors as passive energy storage elements, stored in electric fields. Explains two-plate capacitors, dielectric materials, and capacitance C=Q/V, plus fixed and variable types and op-amp applications.

Learn capacitor fundamentals: current equals C dv/dt and Q equals CV, derive voltage from current, and energy stored is half C V squared.

Solve capacitor problems by applying Q = C V and energy = 1/2 C V^2. Use i = C dV/dt to find current, and compare AC versus DC behavior.

Compute the equivalent capacitance for parallel and series capacitor networks, replacing complex circuits with a single equivalent capacitor using the sum for parallel and the reciprocal rule for series.

Compute the equivalent capacitance for mixed series and parallel configurations, then apply Q = C V to find voltages across each capacitor.

Explore inductors, passive elements that store energy in magnetic fields, learn the V = L di/dt relationship and the energy 1/2 L I^2, and differentiate ideal from non-ideal inductors.

Explore solved examples on inductors, calculating voltage v = L di/dt and energy 1/2 L i^2, and derive current and capacitor-inductor energy in DC circuits.

Learn how to compute equivalent inductance for series and parallel inductors using L_eq = sum and 1/L_eq = sum of reciprocals, and apply delta-star transformations across resistors, inductors, and capacitors.

Explore solved examples of series and parallel inductors, calculate equivalent inductances, and analyze currents and voltages over time using L di/dt and a step-by-step approach.

An op-amp integrator uses a capacitor in the feedback to make the output equal to the negative integral of the input; a summing variant combines multiple inputs.

Learn how a differentiator turns an inverting amplifier into a circuit whose output equals the negative RC times the derivative of the input, i.e., v_out = -RC dv_in/dt.

Explore first-order circuits formed by combining two passive elements, such as RC or RL networks, and learn their first-order differential equations and source-free versus forced excitation.

Explore how a source-free RC circuit produces the natural response as a charged capacitor discharges through a resistor, governed by the time constant RC and exponential decay.

This source-free rc circuit example derives capacitor voltage decay and a 2.4-second time constant; it then uses voltage division to find the voltage across 12 ohms and the current ix.

Analyze a source-free RC circuit as the switch opens, with a 15-volt initial capacitor voltage and decay governed by a 0.2-second time constant from 10 ohm and 20 mF.

Release energy stored in the inductor into the resistor after disconnection in a source-free rl circuit, and the current decays exponentially with a time constant L/R.

Analyze a source-free rl circuit with an initially charged inductor, derive i(t)=10 e^{-2t/3} A, compute tau=3/2 s, and determine v_L and branch currents via equivalent resistance.

An example of a source-free RL circuit, determine initial inductor current in steady state using short-circuit behavior, compute the time constant with equivalent resistances, and express i(t)=I0 e^{-t/τ} after switching.

Explain the step response of an rc circuit, where a capacitor charges from its initial voltage toward the supply via a decaying exponential, highlighting transient and steady-state behavior.

Explore the step response of an RC circuit, with the capacitor voltage moving from 15 V to 30 V in a 2 s time constant.

Analyze the step response of an RC circuit as a 30-volt step is applied, deriving the capacitor voltage and current before and after switching, and the circuit time constant.

Explore the step response of an RL circuit, deriving i(t) as the sum of transient and steady-state components, with initial and final currents and the time constant τ = L/R.

Examine the step response of an RL circuit, tracing how the inductor current evolves after switching, including initial and steady-state currents, short-circuit conditions, and the time constant tau.

Analyze the step response of a two-switch RL circuit, deriving the current in the inductor across three time regions by applying continuity and capturing initial, transient, and steady-state values.

Explore the source-free series resistor-inductor-capacitor circuit, deriving its second-order natural response via kirchhoff's voltage law, with initial capacitor voltage and inductor current, and analyze damping regimes (alpha and omega_n).

In the source-free series rlc circuit, the overdamped case (alpha > omega naught) yields two negative real decaying exponentials, producing a purely transient current with zero steady-state.

Explore solving a source-free series RLC circuit after switching, deriving the current as a sum of two decaying exponentials with overdamped dynamics and initial conditions from steady-state.

Analyze the source-free parallel RLC circuit using Kirchhoff's current and voltage laws, with a charged capacitor and initial inductor current, deriving the voltage equation and relating to the series case.

Analyze a source-free parallel rlc circuit to find capacitor voltage and inductor current at switching using V0 and I0, and derive the damped voltage response V(t) with S1 and S2.

Explore the step response of a parallel RLC circuit, deriving i(t) in the inductor and iR(t) in the 40-ohm resistor from switching and a 20 V capacitor initial condition.

Differentiate AC from DC by examining sinusoidal waveforms and the role of phase and angular frequency. Understand how resistive, inductive, and capacitive loads cause leading or lagging phase shifts.

solve examples on sinusoidal signals, determining amplitude, phase, period, and frequency; convert between sine and cosine forms and compare voltages to identify phase shift and leading/lagging relationships.

Convert AC voltages and currents into phasors to capture amplitude and phase. Explore rectangular, polar, and exponential forms and apply Euler's identity to time-domain signals.

Solve phasor problems by converting polar to rectangular, adding vectors, and converting back to polar with magnitude and phase. Convert sinusoids to phasors and time-domain forms.

Explore phasor relations in AC circuits, converting time-domain signals to frequency domain. See how resistors, inductors, and capacitors link voltage and current through impedance, with inductors leading and capacitors lagging.

Explore impedance and admittance in AC circuits, using Z and Y from resistance, inductance, and capacitance. Learn reactance, magnitude and phase forms, and DC and high-frequency limits.

Analyze Kirchhoff's laws in the frequency domain, compute impedance in series and parallel, and apply voltage and current division, nodal analysis, and Y and delta transformations.

Solve example 1 by converting the circuit to the frequency domain at omega 50 rad/s, then compute Z1, Z2, Z3 and their equivalent impedance.

Explore voltage division in an AC circuit by converting the supply and components to frequency-domain impedance and computing the parallel impedance of the capacitor and inductor to obtain vout.

Learn to calculate circuit current by finding the equivalent impedance through star-delta conversion, series and parallel simplifications, then divide V supply by Z to obtain magnitude and phase.