COURSE 8 FEE
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Questions and Answers

What happens to the voltage across an inductor when the current through it is constant (DC circuit)?

  • The voltage fluctuates randomly.
  • The voltage increases linearly with time.
  • The voltage is zero. (correct)
  • The voltage is equal to the current multiplied by the inductance.

    • What is the nature of an inductor as a circuit element?

  • An active, reactive element that generates power.
  • A passive, reactive element that stores magnetic energy. (correct)
  • A passive element that dissipates power.
  • An active element that dissipates power.

    • In a system of two coupled inductors, which of the following best describes the relationship between their voltages and currents?

  • The voltage across one inductor only depends on the absolute value of the current through both inductors.
  • The voltage across each inductor depends only on the current through itself.
  • The voltage across one inductor depends on the rate of change of current through both inductors. (correct)
  • The voltage across each inductor depends only on the current through the other inductor.

    • What does it mean when inductors are 'coupled'?

    <p>They have a magnetic interaction which affects each other's behavior. (C)</p> Signup and view all the answers

    What does the symbol 'M' represent in the context of two coupled inductors?

    <p>The mutual inductance between the two inductors. (B)</p> Signup and view all the answers

    What is a key characteristic of a circuit in a 'variable state'?

    <p>Current and voltage vary with time. (C)</p> Signup and view all the answers

    What is the relationship between the current through a capacitor and the voltage across it?

    <p>Current is directly proportional to the rate of change (derivative) of voltage. (C)</p> Signup and view all the answers

    What units are used to quantify capacitance?

    <p>Farads [F] (B)</p> Signup and view all the answers

    What is the behavior of the capacitor in a DC circuit (when the voltage is constant)?

    <p>It acts as an open circuit, blocking current flow. (C)</p> Signup and view all the answers

    Which of the following is NOT a characteristic of the voltage across a capacitor?

    <p>It can have sudden jumps at initial time. (D)</p> Signup and view all the answers

    What is the fundamental characteristic of an inductor, as described in the text?

    <p>Voltage across the inductor depends on the rate of change (derivative) of the current through it. (C)</p> Signup and view all the answers

    In what units is inductance measured?

    <p>Henrys [H] (A)</p> Signup and view all the answers

    Which statement is true regarding the current flowing through an inductor, as described in the text?

    <p>The current through an inductor has a continuous variation in time. (D)</p> Signup and view all the answers

    Study Notes

    Electrical Engineering 1 - EE1

    • Course name: Fundamentals of Electrical Engineering 1 - FEE1
    • Course notes by: Assoc. Prof. PhD. Eng. Mihai Iulian REBICAN
    • Course years: 2024-2025

    Electric Circuits in Variable State

    • Variable state circuits: Current and voltage in elements are not constant over time. Variations include sinusoidal, exponential, step, and more.
    • First Kirchhoff's Theorem: The sum of currents entering a node equals zero. Σ 𝑖(𝑘)(𝑡) = 0
    • Second Kirchhoff's Theorem: The sum of voltages around a closed loop equals zero. Σ 𝑣(𝑘)(𝑡) = 0
    • Power of a one-port element: p(t) = u(t)⋅i(t)

    Ideal Passive Circuit Elements

    Resistor

    • Equation: u(t) = R⋅i(t)
    • Power: p(t) = R⋅i²(t)

    Capacitor

    • Equation: i(t) = C(du(t)/dt) (for receiver convention) or i(t) = -C(du(t)/dt) (for generator convention)
    • Voltage across capacitor: u(t) = (1/C)∫i(t)dt + u(t₀)
    • Capacitor is a symmetric element
    • In DC circuits, capacitor acts as an open circuit.

    Inductor

    • Equation: u(t) = L(di(t)/dt) (for receiver convention) or u(t) = -L(di(t)/dt) (for generator convention)
    • Current through inductor: i(t) = (1/L)∫u(t)dt + i(t₀)
    • Inductor is a symmetric element
    • In DC circuits, inductor acts as a short circuit.

    Energetic Characterization

    • Capacitor: Electric energy stored: Wₑ = (1/2)C⋅u²(t)
    • Inductor: Magnetic energy stored: Wₘ = (1/2)L⋅i²(t)

    Coupled Inductors

    • Mutual inductance: Exists between two or more inductors if a changing current in one of them creates a changing magnetic field which influences the current in another.
    • Energy: Wₘ=½Lᵢᵢ₁² + ½L₂ᵢ₂² + Mᵢ₁ᵢ₂
    • Coupling coefficient (k): a measure of the degree of magnetic coupling
    • Perfect coupling (k=1): |M| = √(L₁L₂)
    • No coupling (M=0): Inductors are independent.

    Ideal Active Circuit Elements

    • Ideal voltage source: u(t) = ±e(t)
    • Ideal current source: i(t) = ±j(t)

    Real Branches

    • Combinations of ideal components like resistors, inductors, capacitors, voltage and current sources.
    • Equations become more complex to include initial state effects.

    Real Branches with Magnetic Coupling Inductors

    • Includes the equations for handling magnetic coupling.

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