Sinusoids, Harmonics, and Electrical Power Systems Flashcards

These flashcards cover fundamental mathematical conventions, sinusoidal parameters, electrical power formulas, harmonics, and electromechanical induction principles as detailed in the lecture transcript.

Rounding Convention (2 decimal points)

A value like $0.028$ becomes $0.03$; values from $0.025$ to $0.035$ round to $0.03$, while a value like $0.024$ rounds down to $0.02$.

Microphone

A device that converts sound waves into time-varying electrical signals.

Speaker

A device that converts electrical sinusoids back into sound energy.

Motor

A device that operates using sinusoidal currents to produce mechanical rotation; it converts electrical energy into mechanical energy.

Generator

A device that converts mechanical energy into sinusoidal electrical energy.

Amplitude ($V_p$ or $A$)

Also known as the Peak Voltage, it represents the maximum displacement from zero.

Angular Frequency ($\omega$)

Quantity measured in $rad/s$ and related to frequency by the formula \omega = 2\text{\pi}f.

Phase ($\phi$)

The initial angle of the sinusoid at $t = 0$.

Frequency ($f$)

Measured in Hertz ($Hz$) and defined as $f = \frac{1}{T}$, where $T$ is the time period.

Peak-to-Peak Voltage ($V_{pp}$)

The total vertical distance from the negative peak to the positive peak, calculated as $V_{pp} = 2 \times V_p$.

Periodic Signal

A signal that repeats after a regular interval $T$ such that $v(t + kT) = v(t)$, where $k$ is an integer.

Instantaneous Power ($p(t)$)

Defined as the product of instantaneous voltage and current: $p(t) = v(t) \times i(t)$. For a purely resistive load $R$, $p(t) = \frac{v(t)^{2}}{R}$.

Average Power ($P_{avg}$)

The ratio of energy over time ($P_{avg} = \frac{E}{T}$), which for a sinusoid is $\frac{V_p^{2}}{2R}$.

Root Mean Square (RMS) Value ($V_{rms}$)

The DC equivalent voltage that would produce the same amount of heat or power in a resistor, defined as V_{rms} = \frac{V_p}{\text{\sqrt{2}}} \text{\approx} 0.707V_p.

Fundamental Frequency ($f_0$)

The frequency of the 1st Harmonic (Fundamental Mode), where the wavelength is twice the length of the string ($\lambda_1 = 2L$), calculated as $f_0 = \frac{v}{2L}$.

General Harmonic Rule

The frequency of the $n$-th harmonic is an integer multiple of the fundamental frequency: $f_n = n \times f_0$.

Duty Cycle Percentage

The percentage of time a device is actively 'ON', calculated as $\frac{T_{ON}}{T_{ON} + T_{OFF}} \times 100\%$.

Magnetic Flux ($\Phi$)

A quantity defined by the equation \Phi = BA \text{\cos}(\omega_0 t).

Electromotive Force (EMF, $e$)

Based on Faraday's Law, it is the rate of change of magnetic flux: e = -\frac{d\text{\Phi}}{dt} = BA\text{\omega}_0 \text{\sin}(\text{\omega}_0t).

Inductor

A circuit component where voltage is proportional to the rate of change of current: $v(t) = L\frac{di}{dt}$.

Capacitor

A circuit component where current is proportional to the rate of change of voltage: $i(t) = C\frac{dv}{dt}$.

Potential Difference ($V_{AB}$)

The difference between two points $A$ and $B$, defined as $V_{AB} = V_A - V_B$, calculated by summing voltage gains and drops across a path.