Section 5.7: Inductance
Inductance is a property of a conductor (usually a coil) by which a change in current induces an EMF in itself or in a nearby conductor. It quantifies how effectively a coil resists changes in current.
Key Formulas:
Self-Inductance: \( \mathcal{E} = -L \frac{dI}{dt} \)
Where \( L \) is the inductance in Henry (H), \( \mathcal{E} \) the induced EMF, and \( I \) the current.
Energy Stored: \( U = \frac{1}{2} L I^2 \)
Example 1
A coil of inductance 2 H carries a current increasing at 3 A/s. Find the induced EMF.
\( \mathcal{E} = - L \frac{dI}{dt} = -2 * 3 = -6 \text{ V} \)
Example 2
Calculate energy stored in a 5 H inductor carrying 4 A current.
\( U = \frac{1}{2} L I^2 = 0.5 * 5 * 4^2 = 40 \text{ J} \)
Practice Problems
- An inductor of 3 H experiences a current change of 2 A in 0.01 s. Find induced EMF.
- Energy stored in a 1 H inductor carrying 6 A current?
- Explain how self-inductance opposes current changes in circuits.
- Two coils of inductances 2 H and 3 H are connected in series. Find total inductance.
- A current through an inductor decreases uniformly. Sketch EMF vs time.