Unit 1: DC & AC Circuits Flashcards

Flashcards covering Ohm's law, Kirchhoff's laws, divider rules, RLC series/parallel formulas, AC waveform parameters, power triangle, power factor, and impedance.

What is Ohm's law and what are its key limitations?

Ohm's law states that at constant temperature, the current flowing through a conductor is directly proportional to the voltage across it ($I \propto V$, $I = \frac{V}{R}$, or $V = I R$). Limitations: requires constant temperature, depends on voltage sign, and does not apply to semiconductors, unilateral elements (diodes, transistors), or non-linear elements.

What are Kirchhoff's First and Second Laws as shown in the diagram?

Kirchhoff's First Law (Kirchhoff's Current Law / KCL) states that total current entering a junction must equal total current leaving it. Kirchhoff's Second Law (Kirchhoff's Voltage Law / KVL) asserts that the total sum of all voltages around any closed loop in a circuit must equal zero.

What is Kirchhoff's Current Law (KCL) and how is it expressed algebraically?

KCL states that the algebraic sum of currents meeting at a junction or node in a circuit is zero ($\sum I = 0$). Incoming currents are taken as positive and outgoing currents as negative, so total incoming current equals total outgoing current.

What is Kirchhoff's Voltage Law (KVL) and how are voltage rises and drops treated?

KVL states that at any instant of time, the algebraic sum of voltages in a closed loop is zero ($\sum V = 0$). A transition from -$ to +$is a voltage rise, and$+$to$-$ is a voltage drop, with the sum of voltage rises equaling the sum of voltage drops.

What is the Voltage Division Rule for a series circuit with resistors?

The voltage across any resistor $R_n$ in a series network is given by $V_n = V_{\text{total}} \times \frac{R_n}{\sum R_i}$, where $V_{\text{total}}$ is the total applied voltage and $\sum R_i$ is the total series resistance.

What is the Current Division Rule for two resistors $R_1$ and $R_2$ connected in parallel?

For total circuit current $I$, the branch currents are $I_1 = I \times \frac{R_2}{R_1 + R_2}$ and $I_2 = I \times \frac{R_1}{R_1 + R_2}$.

How do resistors, capacitors, and inductors combine in series and parallel circuits?

Resistors: Series $R_T = R_1 + R_2$, Parallel $\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2}$. Capacitors: Series $\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2}$, Parallel $C_T = C_1 + C_2$. Inductors: Series $L_T = L_1 + L_2$, Parallel $\frac{1}{L_T} = \frac{1}{L_1} + \frac{1}{L_2}$.

What is the RMS value of an AC waveform and its formula for a sinusoidal wave?

The RMS (Root Mean Square) value of AC is the equivalent DC value that produces the same heating effect in a circuit for the same time. For a sinusoidal wave, $I_{\text{rms}} = \frac{I_m}{\sqrt{2}} \approx 0.707\,I_m$.

What is the Average value of an AC current and its formula for a sinusoidal wave?

The average value is the steady DC current that transfers the same total electric charge through a circuit over a half-cycle as the AC current. For a sinusoidal wave, $I_{\text{av}} = \frac{2\,I_m}{\pi} \approx 0.637\,I_m$.

How are Form Factor ($K_f$) and Peak Factor defined for sinusoidal AC quantities?

Form Factor $K_f = \frac{\text{RMS value}}{\text{Average value}} = \frac{0.707\,I_m}{0.637\,I_m} = 1.11$. Peak Factor = \frac{\text{Peak value}}{\text{RMS value}} = \frac{I_m}{I_m / \sqrt{2}} = \sqrt{2} \approx 1.414$$.

What parameters are defined on this sinusoidal AC voltage waveform diagram?

The diagram displays Maximum or Peak Value ($V_m$), RMS Value ($V_{\text{rms}} = 0.707\,V_m$), Average Value ($V_{\text{avg}} = 0.637\,V_m$), Peak to Peak value ($V_{\text{pp}}$), and One complete cycle across $2\pi$.

How are Cycle, Amplitude, Frequency, Time Period, Instantaneous Value, and Peak-to-Peak Value defined?

Cycle: One full set of positive/negative values spanning $360^\circ$ ($2\pi\,\text{rad}$). Amplitude: Maximum positive or negative value. Frequency ($f$): Cycles per second in Hertz ($\text{Hz}$). Time Period ($T$): Time for one complete cycle in seconds. Instantaneous Value: Value at any specific instant ($i = I_m \sin(\theta)$). Peak-to-Peak Value ($I_{\text{pp}}$): Sum of positive and negative peak values.

What are Real Power, Reactive Power, and Apparent Power in AC circuits?

Real Power ($P = V I \cos(\phi)$, in Watts) is dissipated in resistance doing actual work. Reactive Power ($Q = V I \sin(\phi)$, in VAR) flows back and forth due to reactances without doing useful work. Apparent Power ($S = V I$, in VA) is the product of RMS voltage and current.

What graphical relationship is represented by the Power Triangle?

The Power Triangle shows the right-triangle relationship between Real Power ($P = V I \cos(\phi)$), Reactive Power ($Q = V I \sin(\phi)$), and Apparent Power ($S = V I$), satisfying $S^2 = P^2 + Q^2$ or $S = \sqrt{P^2 + Q^2}$.

What is Power Factor and why is maintaining a high power factor important?

Power factor is \cos(\phi) = \frac{\text{Real Power }(P)}{\text{Apparent Power }(S)}. Improving power factor close to unity maximizes power utilization efficiency, reduces cable and equipment power losses, and lowers electricity bills by avoiding utility penalties.

What is Impedance ($Z$) and how is it derived from the Impedance Triangle?

Impedance is the total opposition to AC current flow ($Z = R + jX_L$ or $Z = R - jX_C$). In the impedance triangle, magnitude $Z = \sqrt{R^2 + X^2}$ and Power Factor = \cos(\phi) = \frac{R}{Z}.

What determines whether a circuit has a lagging or leading power factor?

In circuits with net inductive reactance ($X_L$), current lags voltage, giving a lagging power factor. In circuits with net capacitive reactance ($X_C$), current leads voltage, giving a leading power factor.