- Inductors opposite sudden current changes - After connecting, huge back EMF creates voltage in the opposite direction until the inductor is reaches it's steady state - After it reaches it steady state, it behaves like a short circuit - When current decreases, the collapsing magnetic field induced voltage that aids the current direction - trying to keep current flowing - Induced voltage acts as a mini power source $ E=\frac{1}{2}LI^2 $ Magnitude of induces EMF is related to the rate of change of current through it $ V=L \frac{di}{dt} $ Inductance L measures how effectively an inductor can store energy in its magnetic field and oppose changes in current, measured in Henry (H). An inductor has an inductance of 1 Henry if an EMF of 1 volt is induced when the current through it changes at a rate of 1A per second. Typical inductors have values from $1 \micro H$ (high-frequency circuits) to $20 H$ (power and filter applications). Calculations for inductors in series/parallel behave like resistors (non-examinable) KVL (for $r\geq 0$) $ V=L\frac{di}{dt}+iR $ When the switch is first closed, the supply voltage appears entirely across the coil. However the current cannot rise instantly due to back EMF: $ e_{L}=-L \frac{di}{dt} $ The negative sign shows that the induced EMF opposes the change in current. Time constant of an LR circuit defines how quickly the current builds up or decays. Given by: $ \tau = \frac{L}{R} \text{ seconds} $ **Back EMF across inductor** $ V_{L}=V e^{-Rt/L} =Ve^{-t/\tau} $ **Growth of voltage across resistor** $ V_{R}=V(1-e^{-Rt/L})=V(1-e^{-t/\tau}) $ **Growth of current though the circuit** $ i=I(1-e^{-Rt/L})=I(1-e^{-t/\tau}) $