Foundations of Electrical Circuits - DC Circuits

Explore what an electrical circuit is as a closed loop network that provides a return path for current through interconnected elements, demonstrated with a battery, a bulb, and wiring.

Explore the si system and its seven basic units with symbols like meter M and kilogram KG, and learn kilo and milli prefixes to convert 200,000 m to 200 km.

Explore electric charge, measured in coulombs, and how current flows opposite to electron motion. Distinguish direct and alternating current, and apply I = dq/dt and Q = ∫ i dt.

Voltage is the energy to move a unit charge and the pressure driving current, measured in volts (V); VAB is the potential difference between A and B with polarity.

Define power as the rate of energy transfer, measured in watts, and energy as the movement of electrons, measured in joules, with P = VI and energy = P t.

Explore active and passive circuit elements, highlighting active sources—independent and dependent voltage and current sources—and identify the four dependent source types.

Explore ohm's law and resistance, define R as the material's opposition to current, and derive V = IR and R = V/I, including short and open circuits.

Identify branches, nodes, and loops in dc circuits, and apply the fundamental theorem of network topology to determine independent loops and the series and parallel relationships.

Explore Kirchhoff's laws, including Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL), and learn to analyze circuits with Ohm's law, node currents, and voltages through practical examples.

Analyze series resistors and compute voltage shares using V1 equals R1/(R1+R2) times V and V2 equals R2/(R1+R2) times V.

Learn how current divides in parallel resistors, with formulas for I1 and I2, and compute an equivalent resistor using 1/R_eq = 1/R1 + 1/R2, extendable to three resistors.

Apply nodal analysis to determine node voltages using reference ground and non-reference nodes, applying Kirchhoff's current law and Ohm's law in a step-by-step example.

Identify supernodes and apply nodal analysis with voltage sources by using kcl and kvl to solve for node voltages v1, v2, and v3.

Learn to apply mesh analysis to find mesh and branch currents by assigning mesh currents, applying Kirchhoff's voltage law (KVL), and using Ohm's law in a two-mesh circuit.

Use mesh analysis with current sources. A single-mesh source fixes that mesh current; a source between two meshes forms a super mesh solved by KCL and KVL.

Understand the linearity property of a linear dc circuit, where the output current is directly proportional to the input voltage, as 10 V yields 2 A.

Apply the superposition principle to sum voltages or currents from independent sources in a linear circuit. Turn off all but one source, analyze with nodal or mesh methods, then sum.

Transform a voltage source in series with resistor into a parallel current source. Use I = V/R and V = IR to verify equivalence, then find V0 = 3.2 V.

Use Thevenin's theorem to replace a linear two-terminal circuit with a voltage source in series with a resistor, then compute load current using the equivalent circuit.

Apply Norton's theorem to replace a linear two-terminal network with a current source in parallel with a resistor, R_n, found by turning off independent sources, and I_n from short-circuit current.

Learn how operational amplifiers amplify the difference between inverting and non-inverting inputs, achieve high gain, and determine closed-loop gain using a non-ideal model with KCL analysis.

Discover how an ideal op amp, with infinite input resistance and zero input current, yields near equal input voltages and a gain of nine in a simple resistor circuit.

The inverting amplifier uses an op amp with a feedback resistor rf and input resistor r1 to invert and amplify vi. Under the ideal op amp, vo = -(rf/r1) vi.

Explore non-inverting amplifiers that use an op amp with feedback and a resistor network to amplify input signals without inversion, using vo = (1 + rf/r1) vi.

Explore how a summing amplifier uses an op amp with multiple input resistors and a feedback resistor to produce a weighted algebraic sum at the output.

Learn how a difference amplifier uses an op amp to amplify the difference between two inputs while rejecting common signals, with resistor relationships and example design.

Explore how capacitors store energy with two plates and dielectric, using Q = CV and C = Q/V, and apply i = C dv/dt and W = 1/2 C V^2.

Examine series capacitors with C1 and C2 in a circuit, and replace them by an equivalent capacitor Q using 1/Q = 1/C1 + 1/C2; extend to C3 similarly.

Learn how parallel capacitors form an equivalent capacitor by summing C1 and C2 to get Ceq (and add C3 for three capacitors) in circuits.

Explore how inductors store energy in a magnetic field around a coil and core, and learn inductance in henries with v = L di/dt and w = 1/2 L I^2.

Learn how series inductors combine into an equivalent inductance. Apply Leq = L1 + L2 (and Leq = L1 + L2 + L3 for three inductors) to simplify series circuits.

Explore how two inductors in parallel combine into an equivalent inductance using 1/L_eq = 1/L1 + 1/L2, and extend the same approach to three inductors.

Study the natural (transient) response of a source-free RC circuit, where the DC source is disconnected and the capacitor voltage decays as V(t)=V0 e^{-t/τ} with τ=RC.

Explore source-free RL circuits and their natural response, deriving the time constant tau = L/R and the current i(t) = i0 e^{-t/τ} through an RL example.

Explore the step response of an RC circuit, from initial capacitor voltage and switch action to final Vs, highlighting transient and natural responses that combine into the forced (steady-state) response.

Understand the step response of an RL circuit by analyzing initial and final currents and the total solution V/R + (I0 − V/R) e^(−t/τ), with τ = L/R.

Explore the source-free series RLC circuit, featuring resistor, inductor, and capacitor, and learn about natural frequencies S1 and S2, damping factor alpha, and the overdamped, critically damped, and underdamped cases.

Explore the source-free parallel RLC circuit with resistor, inductor, and capacitor in parallel, and its natural responses, including overdamped, critically damped, and underdamped, with alpha, omega0, and omegaD formulas.

Explore the step response of a series RLC circuit, covering overdamped, critically damped, and underdamped cases with a practical 24 V example.

Examine the step response of a parallel RLC circuit, combining first and natural responses, and cover overdamped, critically damped, and underdamped cases with a detailed numerical example.