Electrical Circuits: Inductance and Oscillations
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Questions and Answers

What is the expression for the current intensity $i(t)$ in relation to the inductance $L$ and resistance $R$?

  • $L \frac{di}{dt} + Ri = E$ (correct)
  • $L\frac{di}{dt} = E - Ri$
  • $Ri + L \frac{di}{dt} = 0$
  • $L \frac{di}{dt} - Ri = E$
  • What is the value of the inductance $L$ if the voltage across the resistor is $U_R = 2.7V$ at $t = 2ms$?

  • $0.1\,H$
  • $0.04\,H$ (correct)
  • $0.02\,H$
  • $0.07\,H$
  • What is the formula for the magnetic energy stored in the coil at time $t = 2ms$?

  • $Li$
  • $\frac{1}{2}Ri^2$
  • $\frac{1}{2}Li^2$ (correct)
  • $\frac{1}{2}C(U_C)^2$
  • In an LC circuit, if the capacitance $C = 10 \mu F$, what is the expression for the energy stored in the capacitor?

    <p>$\frac{1}{2}CU^2$</p> Signup and view all the answers

    What is the relationship established between the energy in the capacitor and the coil in an LC circuit?

    <p>Total energy is conserved between capacitor and coil</p> Signup and view all the answers

    Study Notes

    Exercise 1: Establishing Current in a Coil

    • Circuit Components: A coil with inductance L, resistor R = 150Ω, and a battery with electromotive force E = 6V.

    • Initial Conditions: At time t = 0, the circuit is closed.

    • Voltage Across Resistor: The voltage across the resistor reaches UR = 2.7V at t = 2ms.

    • Task 1: Derive the differential equation for the current i(t).

    • Task 2: Calculate the inductance L.

    • Task 3: Determine the magnetic energy stored in the coil at t = 2ms.

    Exercise 2: LC Circuit Oscillations

    • Capacitor Characteristics: A capacitor with capacitance C = 10µF is part of the circuit.

    • Task 4: Express the energy of the capacitor.

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    Description

    This quiz covers essential concepts in electrical circuits, focusing on inductance, resistors, and capacitor characteristics. You'll derive differential equations, calculate inductance, and analyze energy in both coils and capacitors. Perfect for those studying circuit theory and oscillations in physics.

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