The Complete Electric Circuits Course

Apply Kirchhoff’s current and voltage laws to form mesh equations, using consistent loop directions, sign conventions, and Ohm’s law to solve for loop currents.

Learn to calculate the equivalent resistance by applying series and parallel rules, examining short circuits at R=0 and open circuits at R=∞ through a practical example.

Learn to solve circuits with mesh analysis and current sources by forming a supermesh, defining loop currents I1, I2, I3, and solving the resulting equations to find all branch currents.

Explore a transistor example that uses beta relations to relate Ib, Ic, and Ie and solves with mesh analysis rather than nodal analysis, yielding base, collector, and emitter currents.

Explore Norton’s theorem by transforming Thevenin equivalents into Norton equivalents using open and short circuits. Learn to compute Norton current and resistance with nodal analysis and circuit simplifications.

Apply the Thevenin equivalent to find R_th and V_th, then show that maximum power occurs when R_load = R_th, with P_max = V_th^2/(4 R_th).

Identify the op-amp configuration as a difference amplifier and apply the memorized error formula with the given resistors to obtain a 4 millivolts error.

Apply sinusoidal source transformation to convert voltage and current sources, solve for x using impedances, and express results in polar or rectangular form.

The derivative is the gradient of the tangent to f at x, written f'(x) or dy/dx. A function must be continuous at a to be differentiable there.

Explore piecewise functions using the absolute value example f(x)=|x+2|. Derive a two-branch graph: x+2 for x >= -2 and -x-2 for x < -2, ensuring all outputs stay nonnegative.

Master solving inequalities by applying rules, factoring polynomials, and analyzing signs of the rational expression (x^2+3x+2)/(x^2+16) to identify zeroes, exclusions, and nonnegative intervals.

The intermediate value theorem guarantees that a function continuous on [a, b] attains every value between f(a) and f(b) at some c in [a, b].

Explore composite functions by composing f with g (f(g(x))) and applying substitution rules, showing how the domain of f∘g depends on the range of g, which is x ≤ 2.

Discover the conditions for continuity at a point, including f(a) defined, limit exists, and limit equals f(a). Learn about removable, infinite, and jump discontinuities, and continuity from right or left.

Demonstrates the derivative of sin x from first principles using the limit definition and trig identities to show d/dx sin x = cos x.

Explore radian measure by deriving theta as arc length over the radius, linking arc length, radius, and circumference, including the equivalences 360° = 2π radians and 180° = π radians.

Explore the symmetry of functions, including even functions with f(x) = f(-x) and odd functions with f(-x) = -f(x), illustrated by parabola reflection about the y-axis.