Mastering Linear Circuits: Fundamentals

Explore power and energy in electric circuits, linking instantaneous power to voltage and current, and examining active and reactive power across resistors, inductors, and capacitors, with energy as accumulated power.

Explore core waveforms in linear circuits, from direct-current and periodic sine waves to modulated, aperiodic, and impulse shapes, including triangular and time-segmented zero regions.

Learn the effective value of AC, its relation to a sinusoidal rms, and how i_rms = i_max / sqrt(2) yields the same DC power, P = R i_rms^2.

Analyze a sawtooth current through a 6 ohm resistor to find irms and average power, deriving irms = 10/√3 and power = R times irms^2.

this lecture shows how to compute rms voltage and average power in an ac circuit with a six ohm resistor from a given voltage waveform by integrating v^2 over time.

Explore Kirchhoff's current law and Kirchhoff's voltage law, applying nodal and loop analysis to circuit analysis, with sign conventions for currents and voltages.

Apply Kirchhoff's laws to analyze series circuits and find equivalent components: sum of series resistances, sum of series inductances, and reciprocal sum for series capacitors.

Explore the parallel combination of resistor, inductor, and capacitor using KCL and KVL, and derive the equivalent resistance, inductance, and capacitance under nodal and loop analysis.

Apply Kirchhoff's current and voltage laws via nodal analysis to a parallel inductor circuit, find i1(0) and i1(t) from I(t) and i2(t), and compute v1 and v2.

Apply kcl and kvl to a steady-state current-source circuit. Treat the inductor as short and the capacitor as open to determine voltages and stored energy.

Explore non-ideal current and voltage sources, their internal resistances, how loads affect current or voltage, and learn source transformations between current and voltage forms.

Learn to compute power in linear circuits using p = vi or i^2 r, applying Kirchhoff's voltage law to a first circuit and then using conductance to analyze the second.

Compute the power in a resistor from a source using current and voltage, apply nodal analysis to find current, then differentiate power with respect to resistance to locate the maximum.

Analyze resistive networks using voltage dividers in series and current dividers in parallel, applying Kirchhoff's voltage law and Ohm's law to find voltages and currents across resistors.

Analyze resistive networks to compute power losses in a 10 km line with 2-ohm segments, comparing 10 kV and 1 kV sources while deriving current, voltage drops, and loss percentages.

Explore RC networks with capacitors and resistors, analyze transient and steady-state responses using Kirchhoff's laws, and differentiate homogeneous and forced solutions in single-loop RC circuits.

Practice problem guides solving an RC network by finding equivalent resistance, using v_c = v0 e^{-t/τ} with τ = RC, and applying a voltage divider and i_c = C dv_c/dt.

Analyze RL networks in a single-loop circuit with inductors and resistors. Derive the transient current i_L(t) and tau = L/R, and explain homogeneous and forced solutions for dc excitation.

Analyze an RL circuit with a switch, determine the transient and steady-state currents, yielding i_L(t)=2+3 e^{-15 t}, with i_ss=2 A and τ=1/15 s.

Analyze a series rlc network using kirchhoff's voltage law, expressing vr, vl, and vc through i. Derive a second-order differential equation and describe transient and steady-state solutions.

Practice a series rlc circuit with no source, deriving the charge and current. Obtain q(t)=5e^{-2t}-2e^{-5t} and i(t)=-10e^{-2t}+10e^{-5t} from initial conditions q(0)=3, i(0)=0.

Derive the steady-state current for a series RLC network using Ohm's law and Kirchhoff voltage law, yielding i(t)=50 sin 2t - 50 cos 2t and a phase-shifted sinusoid.