Understand how inductors store energy in magnetic fields and their behavior in circuits
An inductor is a coil of wire that stores energy in a magnetic field when current flows through it. Inductance (L) is measured in henries (H).
Induced Voltage (Faraday's Law):
$$V_L = -L\frac{dI}{dt}$$
The voltage across an inductor is proportional to the rate of change of current.
The energy stored in an inductor's magnetic field is:
$$E = \frac{1}{2}LI^2$$
Where E is energy (joules), L is inductance (henries), and I is current (amperes)
Example:
A 10mH inductor carrying 2A of current stores:
$$E = \frac{1}{2} \times 0.01 \times 2^2 = 0.02 \text J$$
When current flows through an inductor and resistor in series:
$$I(t) = \frac{V_s}{R}(1 - e^{-Rt/L})$$
The time constant is τ = L/R. Current rises exponentially to its final value.