Oscillations in LC and RLC Circuits · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Charge on a spring: LC ringing and RLC damping

Science · Electricity & Magnetism · ages 20-21
Name ______________________   Date ____________

  1. In the mass on a spring analogy, what does the inductance L correspond to?

    • Spring stiffness
    • Mass
    • Damping force

  2. An ideal LC circuit rings at its natural rate omega0. What is omega0?

    • 1 over sqrt(LC)
    • sqrt(LC)
    • L over C

  3. Adding resistance to an LC circuit makes the oscillation ring forever.

    Circle one:   True   False

  4. You want a circuit that settles fastest without overshooting. Which damping regime do you pick?

    • Critically damped
    • Underdamped
    • Overdamped

  5. In an ideal LC oscillation, the capacitor is fully discharged at some instant. Where is the energy then?

    • All in the capacitor
    • Gone as heat
    • All in the inductor field, current at peak

  6. In the spring analogy for an LC circuit, what does the current correspond to?

    • Position
    • Velocity
    • Force

  7. Starting from the loop rule, which equation governs the charge in an ideal LC circuit?

    • d squared q/dt squared plus (1/LC) q equals 0
    • dq/dt plus R times q equals 0
    • d squared q/dt squared plus R dq/dt equals 0

  8. A student says a resistor shifts omega0 far away but wastes no energy. What is the error?

    • Bigger R raises the resonant rate far above omega0
    • Resistance changes nothing at all
    • Resistance drains energy as heat while the rate stays near omega0
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Charge on a spring: LC ringing and RLC damping W1-mt_QJsqX7xzkZ-s1

  1. Mass · L resists changes in current the way mass resists changes in velocity.
  2. 1 over sqrt(LC) · The loop equation gives omega0 equals 1 over sqrt(LC).
  3. False · Resistance turns oscillation energy into heat, so the ringing decays.
  4. Critically damped · Critical damping is the boundary choice that settles quickest with no overshoot.
  5. All in the inductor field, current at peak · Empty capacitor means zero electric storage, so all energy rides the magnetic field.
  6. Velocity · Current is the rate of charge flow, just as velocity is the rate of position change.
  7. d squared q/dt squared plus (1/LC) q equals 0 · Drops sum to zero with no R term, leaving the pure spring equation.
  8. Resistance drains energy as heat while the rate stays near omega0 · R steals energy as heat each cycle. The oscillation rate stays near omega0.
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