Introduction to Electrical Concepts and Analysis

Comprehensive practice flashcards covering fundamental electrical quantities, DC circuit laws, AC analysis, electrical machines, and electronics (diodes and op-amps) based on the lecture transcript.

What is the SI unit and unit symbol for electric charge?

coulomb ($C$)

According to the lecture, why are 3 or 4 significant figures typically used in calculations?

Because we are generally only able to measure quantities like voltage, current, or resistance to 3 or 4 significant figures of precision, and more may give an incorrect impression of the result's precision.

What is the value of the charge of a single electron?

$$-1.60 \times 10^{-19}\,C$$

How is current ($i$) defined in terms of charge ($q$) and time ($t$)?

$i = \frac{dq(t)}{dt}$ ($A$)

In circuit theory, when is the value of current ($i$) considered positive in a reference direction?

If positive charges are moving in the direction of the arrow, or negative charges are moving in the opposite direction to the arrow.

What is the unit of voltage ($V$), and what is its equivalent in Joules and Coulombs?

The volt ($V$), which is equivalent to $J \cdot C^{-1}$.

What does the 'ground' symbol in a circuit diagram indicate?

It indicates the reference point for the circuit, where the voltage is taken to be $0\,V$. Elevations of potential ($V_A$, $V_B$, etc.) are measured relative to this point.

What characterizes a circuit that is described as 'floating'?

A circuit with no actual physical connection to the ground, which can accumulate a static charge and reach any potential relative to ground.

What is the 'passive reference configuration' for a circuit element?

A configuration where the reference direction for the current $i$ enters the terminal marked with the positive ($+\text{sign}$) of voltage $v$, such that power absorbed is $p = v \times i$.

State Kirchhoff’s Current Law (KCL).

The sum of currents entering any node is zero.

State Kirchhoff’s Voltage Law (KVL).

The sum of voltages around any loop is zero.

What occurs when two circuit elements are in series?

They share the same current flowing through them.

What occurs when two circuit elements are in parallel?

They have the same voltage across them.

What is Ohm's Law for a resistor in passive reference configuration?

$$v = i \times R$$

How is conductance ($G$) defined and what is its unit?

Conductance is the reciprocal of resistance ($G = 1/R$), measured in siemens ($S$).

What is the formula for the electrical resistance of a conductor with uniform cross-sectional area ($A$) and length ($l$)?

$R = \rho \frac{l}{A}$, where $\rho$ is the resistivity of the material.

What are the formal definitions of an open circuit and a short circuit?

An open circuit has zero current regardless of voltage ($R = \infty\,\Omega$); a short circuit has zero voltage regardless of current ($R = 0\,\Omega$).

What is the formula for the equivalent resistance ($R_{eq}$) of $n$ resistors in parallel?

$$R_{eq} = \left( R_1^{-1} + R_2^{-1} + \dots + R_n^{-1} \right)^{-1}$$

What is the Voltage Divider equation for the voltage $V_1$ across resistor $R_1$ in series with $R_2$?

$$V_1 = V \frac{R_1}{R_1 + R_2}$$

What is the Current Divider equation for the current $I_1$ through resistor $R_1$ in parallel with $R_2$?

$$I_1 = I \frac{R_1^{-1}}{R_1^{-1} + R_2^{-1}}$$

What does the 'storage capacity' of a battery measured in ampere-hours ($A \cdot h$) represent?

It represents the total stored charge ($Q$). $1\,A \cdot h$ is equal to $3600\,C$.

State the Maximum Power Transfer Theorem for a supply with source resistance $R_s$ and a load resistance $R_l$.

Power delivered to the load is maximized when the load resistance is matched to the source resistance ($R_l = R_s$), resulting in $50\%$ efficiency.

What is the fundamental 'capacitor equation' defining current ($i$)?

$$i = C \frac{dv}{dt}$$

How does an ideal capacitor behave at DC steady state?

It behaves like an open circuit ($i = 0$ because $\frac{dv}{dt} = 0$).

What is the formula for energy ($w$) stored in a capacitor?

$$w = \frac{1}{2} C v^2$$

What is the time constant ($\tau$) for an RC circuit?

$$\tau = RC$$

What is the fundamental 'inductor equation' defining voltage ($v$)?

$$v = L \frac{di}{dt}$$

How does an ideal inductor behave at DC steady state?

It behaves like a short circuit ($v = 0$ because $\frac{di}{dt} = 0$).

What is the formula for energy ($E$) stored in the magnetic field of an inductor?

$$E = \frac{1}{2} L i^2$$

What is the time constant ($\tau$) for an RL circuit?

$$\tau = L/R$$

What is the relationship between frequency ($f$) and angular frequency ($\omega$) in AC circuits?

$$f = \frac{\omega}{2\pi}$$

What is the root-mean-square (rms) voltage ($V_{rms}$) for a sinusoidal voltage with peak amplitude $V$?

$$V_{rms} = \frac{V}{\sqrt{2}} \approx 0.707V$$

How is a phasor represented from a sinusoidal signal $v(t) = V \cos(\omega t + \phi)$?

$$\mathbf{V} = V \angle \phi$$

What is the complex impedance ($Z_L$) of an inductor in a steady state sinusoidal system?

$$Z_L = j \omega L$$

What is the complex impedance ($Z_C$) of a capacitor in a steady state sinusoidal system?

$$Z_C = \frac{1}{j \omega C}$$

Define 'Real Power' ($P$) and 'Reactive Power' ($Q$) in AC systems.

$P$ is average/real power measured in watts ($W$). $Q$ is reactive power measured in volt ampere reactive ($VAR$).

State the voltage and current relationships for an ideal transformer with a turns ratio $N_1:N_2$.

$V_2 = \frac{N_2}{N_1} V_1$ and $I_2 = \frac{N_1}{N_2} I_1$

What is 'impedance transformation' through a transformer?

A load $Z_L$ on the secondary is seen at the primary as an equivalent impedance $Z'_L = \left( \frac{N_1}{N_2} \right)^2 Z_L$.

What is the formula for the force ($F$) on a current-carrying conductor in a magnetic field?

$$\mathbf{F} = \mathbf{i} \times \mathbf{B} \cdot l$$

How do you calculate the synchronous speed ($n_s$) in RPM for an AC machine with $N$ pole pairs per phase and frequency $f$?

$$n_s = \frac{60f}{N}$$

What are the two fundamental equations for a DC machine relating torque and EMF to current and speed?

$\tau = k \cdot i$ and $E = k \cdot \omega$

What is the transfer function for an ideal operational amplifier in an inverting configuration?

$$v_{out} = -\frac{R_F}{R_A} v_{in}$$

In an ideal op-amp circuit with negative feedback, what are the two assumptions of the 'summing-point constraint'?

1. The voltage at the inverting input equals the voltage at the non-inverting input ($v^- = v^+$). 2. No current flows into the op-amp input terminals.

What is the peak-to-peak ripple voltage ($\Delta v_L$) for a full-wave rectifier with a filter capacitor $C$, load current $i_L$, and period $T$?

$$\Delta v_L = \frac{i_L T}{2C}$$

What is the function of an H-bridge circuit?

It uses four transistors as switches to control both the speed and direction of rotation of a DC motor.