Mechanics, Electrostatics, and Circuits

Linear Distance vs. Time Graph

Graph representing constant, non-zero velocity with zero acceleration

Parabolic Distance vs. Time Graph

Graph representing constant acceleration (quadratic relationship, d ∝ t^2)

Slope of Velocity vs. Time Graph

Acceleration (a = Δv / Δt)

Area Under Velocity vs. Time Graph

Total displacement/distance traveled

Power at Constant Velocity

Mechanical rate of energy transfer calculated as constant force multiplied by constant velocity (P = F * v)

Uniform Electric Field Representation

Parallel and equally spaced electric field lines, proving intensity is identical at all positions

Stored Capacitor Potential Energy

Electrical potential energy calculated as E = 1/2 * C * V^2

Electrical Resistivity (ρ)

Intrinsic material property that is the exact inverse reciprocal of conductivity (ρ = 1/σ)

Resistors in Series

Configuration where resistors add directly (R_tot = R1 + R2) and current is constant throughout

Resistors in Parallel

Configuration that decreases total circuit resistance (1/R_tot = 1/R1 + 1/R2) and voltage is constant across branches

Capacitors in Series

Configuration where capacitors add reciprocally (1/C_tot = 1/C1 + 1/C2)

Capacitors in Parallel

Configuration where capacitors add directly (C_tot = C1 + C2)

Electrical Power Formulas

Circuit rate equations given as P = IV = I^2*R = V^2/R

Period (T) of AC Signal

Total duration required to complete one entire "on" and "off" cycle of an oscillating signal