REE Board Exam flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Quadratic formula

For ax^2 + bx + c = 0, the roots are x = [-b ± sqrt(b^2 - 4ac)]/(2a), provided a is nonzero.

Law of cosines

In any triangle, c^2 = a^2 + b^2 - 2ab cos C, where C is the angle opposite side c.

Derivative of sine

The derivative of sin x with respect to x is cos x; the derivative of cos x with respect to x is -sin x.

Definite integral meaning

A definite integral gives the signed area under a curve between two limits and equals F(b) - F(a) for an antiderivative F.

Conditional probability

P(A|B) equals P(A and B) divided by P(B), for P(B) greater than zero; it gives the probability of A given that B occurred.

Euler's formula

e^(iθ) = cos θ + i sin θ, linking complex exponentials with trigonometric functions and enabling the polar form of complex numbers.

Matrix determinant 2x2

For matrix [[a, b], [c, d]], the determinant is ad - bc; a nonzero determinant means the matrix is invertible.

Circle area and circumference

A circle of radius r has area πr^2 and circumference 2πr; its diameter equals 2r.

Arithmetic mean

The arithmetic mean of n numbers is their sum divided by n; it measures the central tendency of a data set.

Binomial probability

P(X = k) = C(n,k) p^k (1 - p)^(n-k), the probability of exactly k successes in n independent trials with success probability p.

Logarithm product rule

log_b(xy) = log_b(x) + log_b(y), for positive x and y and base b greater than zero and not equal to one.

Newton's second law

The net force on an object equals its mass times acceleration, F = ma, with force in newtons and mass in kilograms.

Carnot efficiency

The maximum thermal efficiency of a heat engine is 1 - T_C/T_H, where both temperatures are absolute temperatures in kelvin.

First law of thermodynamics

Energy conservation for a system gives ΔU = Q - W, where Q is heat added to the system and W is work done by it.

Ideal gas law

PV = nRT relates pressure, volume, amount in moles, and absolute temperature; R is 8.314 J/(mol·K).

Bernoulli equation

For steady, incompressible, frictionless flow, P + (1/2)ρv^2 + ρgh remains constant along a streamline.

Hooke's law stress form

Within the elastic limit, stress equals Young's modulus times strain, σ = Eε, for a material under axial loading.

pH definition

pH equals the negative base-10 logarithm of hydrogen ion concentration in moles per liter: pH = -log[H+].

Avogadro's number

One mole contains 6.022 × 10^23 elementary entities, such as atoms or molecules, defining the amount of substance.

Static equilibrium

A rigid body remains at rest when the vector sum of forces is zero and the sum of moments about any point is zero.

Continuity equation fluids

For incompressible flow, A1v1 = A2v2, so fluid speed increases where the cross-sectional area decreases.

RMS voltage

For a sine wave, RMS voltage equals peak voltage divided by the square root of two, about 0.707 times peak.

Power factor

Power factor is real power divided by apparent power, equal to the cosine of the angle between voltage and current in sinusoidal circuits.

Inductive reactance

Inductive reactance is X_L = 2πfL, measured in ohms; it increases with frequency and inductance.

Capacitive reactance

Capacitive reactance is X_C = 1/(2πfC), measured in ohms; it decreases as frequency or capacitance increases.

Series resonance frequency

A series LC circuit resonates at f = 1/(2π√(LC)), where inductive and capacitive reactances are equal in magnitude.

Three-phase real power

In a balanced three-phase system, real power equals √3 times line-to-line voltage times line current times power factor.

Transformer voltage ratio

For an ideal transformer, the primary-to-secondary voltage ratio equals the turns ratio: V1/V2 = N1/N2.

Synchronous speed

Synchronous speed of an AC machine is N_s = 120f/P, where f is frequency in hertz and P is pole count.

Per-unit impedance

Per-unit impedance equals actual impedance divided by base impedance, where base impedance is base voltage squared divided by base power.

Power factor correction

Capacitor reactive power needed to raise power factor from cos φ1 to cos φ2 is Q_c = P(tan φ1 - tan φ2).

Three-phase fault current

For a balanced three-phase fault, fault current equals line-to-neutral voltage divided by positive-sequence impedance, or line-to-line voltage divided by √3 times that impedance.