In-depth Notes on Electrical Circuits and Components

Introduction to Components

  • This lecture outlines the basics of electrical circuits which are crucial for students, including topics that may need revision before progressing.

Système International (SI) Units and Common Prefixes

  • Quantities and Symbols:

    • Capacitance (C): Farad (F)

    • Charge (Q): Coulomb (C)

    • Current (I): Ampere (A)

    • Electromotive force (E): Volt (V)

    • Frequency (f): Hertz (Hz)

    • Inductance (self) (L): Henry (H)

    • Period (T): Second (s)

    • Power (P): Watt (W)

    • Resistance (R): Ohm (Ω)

  • Common Prefixes:

    • Tera (T): 101210^{12}

    • Giga (G): 10910^{9}

    • Mega (M): 10610^{6}

    • Kilo (k): 10310^{3}

    • Milli (m): 10−310^{-3}

    • Micro (µ): 10−610^{-6}

    • Nano (n): 10−910^{-9}

    • Pico (p): 10−1210^{-12}

Electrical Circuits

  • Electric Charge:

    • Amount of energy that can be positive or negative.

  • Electric Current:

    • The flow of electrical charge (usually electrons).

    • Components:

    • Direct Current (DC): Current flows in one direction.

    • Alternating Current (AC): Current direction periodically changes.

  • Electromotive Force and Potential Difference:

    • E.M.F. causes current flow and is measured in volts.

    • Potential difference exists between two points in a circuit.

Circuit Representation

  • Voltage Reference Points:

    • All voltages measured with respect to another point, often ground.

  • Circuit Diagrams:

    • Represent voltages and circuit connections using standardized symbols.

Resistors, Capacitors, and Inductors

  • Resistors:

    • Provide resistance, measured in Ohms (Ω).

  • Capacitors:

    • Store energy in an electric field, measured in Farads (F).

  • Inductors:

    • Store energy in a magnetic field, measured in Henrys (H).

Ohm’s Law & Kirchhoff’s Laws

  • Ohm’s Law:

    • I=VRI = \frac{V}{R}; Current is directly proportional to voltage and inversely proportional to resistance.

  • Kirchhoff’s Current Law:

    • I<em>1+I</em>2+I3=0I<em>1 + I</em>2 + I_3 = 0; Total current entering a junction equals total current leaving.

  • Kirchhoff’s Voltage Law:

    • E−V<em>1−V</em>2=0E - V<em>1 - V</em>2 = 0; Total voltage around a loop equals zero.

Power Dissipation in Resistors

  • Power (PP) dissipation given by:

    • P=V⋅IP = V \cdot I

  • Combined with Ohm’s Law gives:

    • P=V2RP = \frac{V^2}{R}

    • P=I2⋅RP = I^2 \cdot R

Resistors in Circuits

  • Series Circuits:

    • Total resistance: R=R<em>1+R</em>2+R3R = R<em>1 + R</em>2 + R_3

  • Parallel Circuits:

    • Total resistance: 1R=1R<em>1+1R</em>2+1R3\frac{1}{R} = \frac{1}{R<em>1} + \frac{1}{R</em>2} + \frac{1}{R_3}

Resistive Potential Dividers

  • Voltage division in a circuit involving resistors:

    • General Case: V<em>2V=R</em>2R<em>1+R</em>2\frac{V<em>2}{V} = \frac{R</em>2}{R<em>1 + R</em>2}

Sinusoidal Quantities

  • Period (T):

    • Time for one cycle.

    • Frequency (f):

    • f=1Tf = \frac{1}{T}; Number of cycles per second.

Circuit Symbols

  • Standard symbols represent components:

    • Resistor, Capacitor, Inductor, Ground, Voltage Source, etc.

Capacitors

  • Function and Measurement:

    • Store electric charges, measured in Farads.

    • Different types include polarized and unpolarized capacitors.

  • Charging and Discharging:

    • Capacitors charge up according to the equation I=(V<em>s−V</em>c)RI = \frac{(V<em>s - V</em>c)}{R}; Voltage across capacitor during charge is Vc=QCV_c = \frac{Q}{C}.

    • The time constant, τ=R⋅C\tau = R \cdot C, defines the rate of charge/discharge.

Uses of Capacitors

  • Applications include timing, smoothing, filtering, and coupling in circuits.