Inductance & Inductors
Faraday's law and Lenz's law; self and mutual inductance; factors affecting the inductance of a coil; the L-R time constant and energy stored in a magnetic field.
Inductance, summary notes
- Faraday's law: the EMF induced in a coil is proportional to the rate of change of flux linkage, EMF = −N·dΦ/dt.
- Lenz's law is the minus sign: the induced EMF always opposes the change that produced it.
- Self-inductance L is measured in henries. The EMF induced by a changing current in the same coil is EMF = −L·di/dt.
- Inductance rises with the SQUARE of the number of turns, with core permeability and with cross-sectional area, and falls with length.
- Energy stored in the magnetic field is E = ½LI².
- The L-R time constant is τ = L / R. Current rises to 63.2% of its final value in one time constant.
- ⚠ Exam trap: Lenz means opposition, and because L ∝ N², doubling the turns roughly quadruples the inductance, not doubles it.
- Faraday's law
- EMF = −N · dΦ/dt
- Self-induced EMF
- EMF = −L · di/dt
- Inductance of a coil
- L = μN²A / l (L ∝ N²)
- Energy stored
- E = ½LI²
- Time constant
- τ = L / R
A coil of 200 turns has an inductance of 4 H. Roughly what inductance results from rewinding it with 400 turns on the same core?
L ∝ N². Doubling the turns multiplies L by 2² = 4, giving approximately 16 H.
A 2 H inductor carries 3 A. Find the energy stored in its magnetic field.
E = ½LI² = 0.5 × 2 × 3² = 0.5 × 2 × 9 = 9 J.
Electromagnetic induction, Faraday & Lenz
Inductance concept map
Inductance
Inductance quiz
Inductance & Inductors, quiz
1. The reactance of a 0.2 H inductor at 50 Hz is about:
62.8 ohms6.28 ohms0.001 ohms2. Two 40 mH inductors in series (no mutual coupling) give a total inductance of:
80 mH20 mH40 mH3. Lenz's law states that an induced EMF:
Opposes the change producing itAlways aids the applied voltageIs proportional to the resistance of the circuit4. A coil of 200 turns has 4 H of inductance. Rewound with 400 turns on the same core it will have approximately:
16 H8 H2 H5. Faraday's law states that induced EMF is proportional to:
The rate of change of flux linkageThe steady value of the fluxThe resistance of the coil6. A 2 H inductor carries 3 A. The energy stored is:
9 J6 J18 J7. The time constant of an L-R circuit is:
L / RR / LL × R8. The unit of inductance is the:
HenryFaradWeber9. Inserting an iron core into an air-cored coil:
Increases its inductanceDecreases its inductanceHas no effect on inductance10. Moving a magnet faster through a coil produces:
A larger induced EMFA smaller induced EMFNo change in EMF