Circuit Analysis Final Review

Circuit Analysis Final Review

• Final Exam: Thursday, Dec 12, 2024, 2:00 PM - 4:30 PM, Location 249B
• Allowed Materials: Calculator, pen, one formula sheet (double-sided), blank sheets for drafting
• Exam Content: 5% before midterm, 95% after midterm
• Question Types: True/False (10), Short Answer (4), Single Selection (10), Calculation (8)

Electrical Variables

• Current: the amount of charge flowing past a point in a certain amount of time. Formula: i = dq/dt
• Voltage: the energy required to move a unit charge from a reference point to another. Formula: v = dw/dq.
• Power: time rate of expending or absorbing energy. Formula: p = dw/dt = dq/dt *v = vi

Reference Direction

• If the calculated value of current (I) or voltage (v) is positive, then the reference direction is consistent with the actual direction.
• If the calculated value of current (I) or voltage (v) is negative, the reference direction is opposite to the actual direction.

Electrical Components

• Wire: Ideal wire has resistance R=0.
• Switch:
  • Open/off = Open circuit
  • Close /on = Short circuit

Independent Voltage/Current Sources

• Voltage Source: Constant voltage source: Voltage is constant. Current will vary depending on circuit.
• Current Source: Constant current source: Current is constant. Voltage will vary depending on circuit.

Dependent Voltage/Current Sources

• A dependent source is one whose value depends on some other quantity in the circuit.

Series & Parallel Resistors

• Series:
  • I = I₁ = I₂ = I₃
  • V = V₁ + V₂ + V₃
  • Req = R₁ + R₂ + R₃
• Parallel:
  • I = I₁ + I₂ + I₃
  • V = V₁ = V₂ = V₃
  • 1/Req = 1/R₁ + 1/R₂ + 1/R₃

Bridge Circuit

• Balanced Bridge: I = 0, V₂ = V₄; R₁R₄ = R₂R₃

Measuring Voltage & Current

• Ideal Ammeter: Equivalent to a short circuit in series with the component.
• Ideal Voltmeter: Equivalent to an open circuit in parallel with the component.

Circuit Analysis - Outline

• Topic 1-2: Prerequisite and resistive circuit and measurements
• Topic 3: Circuit valuable analysis techniques (node voltage method, mesh current method)
• Topic 4: Operational Amplifier
• Topic 5-6: Inductance and Capacitance & RC, RL, RLC Circuit
• Topic 7-8: Sinusoidal steady state analysis and power calculations
• Topic 9-10: Three-phase circuit (balanced) & Mutual inductance

Capacitance

• Q-V Relationship: Q(t) = CV(t)
• 1-V Relationship: i(t) = C dv(t)/dt
• Capacitance in Parallel: Ceq = C₁ + C₂ + C₃
• Capacitance in Series: 1/Ceq = 1/C₁ + 1/C₂ + 1/C₃

Inductance

• V-I Relationship: V(t) = L di(t)/dt

RC & RL Circuits

• RC-Circuit: Resistance and capacitance in series with a voltage source. (Charging & Discharging).
• RL-Circuit: Resistance and inductor in series with a voltage source. (Charging & Discharging).

Source Transformation

• A voltage source in series with a resistor can be replaced by a current source in parallel with the same resistor, or vice versa.

Thevenin's Theorem

• A linear two-terminal circuit can be replaced by an equivalent circuit consisting of an open-circuit voltage source in series with a resistor.

Norton's Theorem

• A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a short-circuit current source in parallel with a resistor.

Maximum Power Transfer

• Maximum power of the load is transferred to the load when the load resistance equals the Thevenin resistance as seen from the load.

Operational Amplifiers

• Ideal Op-Amp Properties:
  • Input currents are zero: I₁ = 0A, I₂ = 0A
  • Input voltage difference is zero: V₂ = V₁

Sinusoidal Steady State Analysis and Power Calculations

• Time Domain: v(t) = Vm cos(ωt + φ)
• Phasor Domain: V = Vm∠φ

Impedance

• Series Impedance: Z = Z₁ + Z₂ + Z₃ + ... + Zn
• Parallel Impedance: 1/Zeq = 1/Z₁ + 1/Z₂ + 1/Z₃ + ... + 1/Zn

Kirchhoff's Laws

• Current Law (KCL): The sum of currents entering a node equals the sum of currents leaving the node.
• Voltage Law (KVL): The algebraic sum of voltages around a closed loop is zero.

Mutual Inductance

• The magnetic flux Φ₁ emanating from coil 1 has two components: one Φ₁₁ links coil 1, and another Φ₁₂ links coil 2. Mutual inductance equation given

Ideal Transformer

• Relationship: V₁/N₁ = V₂/N₂ = I₂/I₁

Three-Phase Circuits

• Y-connected circuits: Line voltage is √3 phase voltage. Line current = phase current
• Delta-connected circuits: Line voltage/phase voltage are identical. Different relationships for currents

Prepare for your Circuit Analysis final exam with this comprehensive quiz. It covers key electrical variables such as current, voltage, and power. Test your understanding through various question formats including True/False, short answers, and calculations.