Worksheet: Self-Inductance of an Inductor

In this worksheet, we will practice calculating a conducting loop's self-inductance from the change rates of emf induced in it and the magnetic field produced by the loop.

Q1:

A coil with a self-inductance of 3.0 H carries a current that decreases at a uniform rate d / d 𝐼 𝑡 = 0 . 0 5 0 A/s. What is the emf induced in the coil?

Q2:

What is the self-inductance per meter of a coaxial cable whose inner radius is 0.500 mm and whose outer radius is 4.00 mm?

  • A 3 . 2 9 × 1 0 7 H/m
  • B 2 . 9 8 × 1 0 7 H/m
  • C 3 . 6 0 × 1 0 7 H/m
  • D 4 . 1 6 × 1 0 7 H/m
  • E 3 . 9 3 × 0 7 H/m

Q3:

An emf of 0.40 V is induced across a coil by changing the current through it. The current changes uniformly from 0.10 A to 0.60 A in 0.30 s. What is the self-inductance of the coil?

Q4:

A 25.0-H inductor has 100 A of current turned off in 1.00 ms. What voltage is induced to oppose this?

  • A 2 . 2 4 × 1 0 6 V
  • B 2 . 1 7 × 1 0 6 V
  • C 2 . 3 6 × 1 0 6 V
  • D 2 . 5 0 × 1 0 6 V
  • E 2 . 4 1 × 1 0 6 V

Q5:

What is the rate at which the current though a 0.30-H coil is changing if an emf of 0.12 V is induced across the coil?

Q6:

The current 𝐼 ( 𝑡 ) through a 7.0 mH inductor varies with time, as shown in the figure. The resistance of the inductor is 4.0 Ω.

Calculate the voltage across the inductor from 𝑡 = 0 . 0 to 𝑡 = 3 . 0 m s .

Calculate the voltage across the inductor from 𝑡 = 3 . 0 m s to 𝑡 = 6 . 0 m s .

Calculate the voltage across the inductor from 𝑡 = 6 . 0 m s to 𝑡 = 1 2 . 0 m s .

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