Self-Inductance and Energy Stored in a Magnetic Field · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Coils fight change: inductance, stored energy, RL circuits

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

  1. An ideal constant-L inductor carries current I. What is its stored magnetic energy?

    • (1/2) L I squared
    • (1/2) L squared I
    • (1/2) L I without the square

  2. Two long air-core solenoids have the same length and cross-sectional area but different turn counts. Which has larger self-inductance?

    • Both have equal inductance at every turn count
    • The solenoid with the smaller turn count
    • The solenoid with the larger turn count

  3. An ideal series RL circuit initially has zero current. Connecting a finite constant emf E makes its current jump immediately to E/R.

    Circle one:   True   False

  4. A uniform magnetic field doubles throughout the same fixed volume of vacuum. What happens to the magnetic energy in that volume?

    • It quadruples
    • It doubles
    • It remains unchanged

  5. An ideal RL circuit has L = 4 H and total R = 2 ohms. What is its time constant?

    • 8 s
    • 2 s
    • 0.5 s

  6. Current through a constant-L coil is increasing. How does its self-induced emf act?

    • It assists the rise and makes the current increase faster
    • It disappears whenever the current changes with time
    • It opposes the increase in current

  7. Opening a switch in a current-carrying inductive circuit can produce a spark. What can initiate conduction across the gap?

    • A large induced voltage from a rapid current decrease
    • Stored charge released by an ordinary resistor at the gap
    • A battery voltage that must rise whenever any switch opens

  8. A student says an ideal RL current rising from zero fully reaches E/R after one tau. Which correction is accurate?

    • It reaches its exact final value only after three time constants
    • It reaches about 63% and approaches its final value asymptotically
    • It reaches about 37% and then stays at that smaller current forever
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Answer key

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

Coils fight change: inductance, stored energy, RL circuits W1-mt_BLyLSJT-Fr-s1

  1. (1/2) L I squared · Integrating absorbed power L I dI/dt while current rises from zero gives U = (1/2) L I squared.
  2. The solenoid with the larger turn count · With material, length and area fixed, L = mu0 N squared A / l increases with N squared.
  3. False · The current starts at zero and approaches E/R. A current jump through an ideal inductor would require an unbounded voltage.
  4. It quadruples · U = B squared V / (2 mu0). With V fixed, replacing B by 2B multiplies U by four.
  5. 2 s · Tau = L/R = 4/2 = 2 s.
  6. It opposes the increase in current · The self-induced emf is -L dI/dt. Its polarity opposes the current increase.
  7. A large induced voltage from a rapid current decrease · A rapid current decrease can produce a large induced voltage. If the gap breaks down, magnetic field energy can feed the spark.
  8. It reaches about 63% and approaches its final value asymptotically · At one tau, I/(E/R) = 1 - exp(-1), about 0.632. The ideal exponential never reaches its limiting value at a finite time.
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