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Self-inductance $L$ measures a coil's tendency to oppose changes in its own current. Defined as $L = N\Phi/I$ (flux linkage per unit current), it produces back-EMF $\varepsilon = -LdI/dt$. Unit: henry (H). The inductor is the magnetic analog of a capacitor — it stores energy in the magnetic field rather than the electric field.

For a solenoid: $L = \mu_0 n^2 V = \mu_0 N^2 A/l$. Key dependencies: $L \propto N^2$ (doubling turns quadruples $L$), $L \propto A$ (larger cross-section), $L \propto 1/l$ (shorter solenoid). With a ferromagnetic core: $L \to \mu_r L$ (enhanced by hundreds or thousands). For a toroid: $L = \mu_0 N^2 A/(2\pi r)$.

LR circuit transients: growth $I = (\varepsilon/R)(1 - e^{-t/\tau})$ with $\tau = L/R$. Decay: $I = I_0 e^{-t/\tau}$. At $t = 0$: inductor acts as open circuit (opposes sudden change). At steady state: acts as short circuit ($dI/dt = 0$).

Series combination: $L_{\text{eq}} = L_1 + L_2 \pm 2M$. Parallel: $1/L_{\text{eq}} = 1/L_1 + 1/L_2$(without coupling). The$\pm 2M$sign depends on relative winding directions — aiding adds, opposing subtracts.$