ECE 201: Lecture 14Borja Peleato1• Inductance and InductorsInductance• In practice, cables have a (tiny) resistance, so thevoltage between both ends of a cable is not zerowhen a current is flowing through them: V=R*I• Apart from this voltage, due to Ohm’s law, thereis another component that we cannot explainwith resistance only– if the current is increasing, the voltage seems to belarger than that predicted by Ohm’s law– If the current is decreasing, the voltage seems to besmaller than that predicted by Ohm’s law• There is a voltage component which isproportional to the rate of variation of thecurrent. The proportionality factor is calledinductance.2Inductors• If you arrange a very long cable into a coil, itpresents a very large inductance– When the current is constant, the voltage is (nearly)zero, because the resistance is very small– When the current changes, a voltage appears. Thefaster the current changes, the bigger this voltage• Inductor:– Ideal representation for a wire without resistancearranged into a coil– Stores magnetic energy (in the form of a magneticfield through the coil)– Represented by L– Units: Henry’s (H)–3ExampleFind the voltage induced in a 250mH inductorwhen the current changes by 50A every second4Integral relationship•• This means that I can find the current from thevoltage, but only up to a certain constant.• i(t0) is called the initial condition. If I want toknow the exact current in an inductor I need toknow the voltage and the initial condition.– Think of it as finding the speed of a car from itsacceleration. You need its initial speed…• Important observations:– The current in an inductor will always be continuous(unless the voltage becomes infinite)– In DC (constant currents and voltages), an idealinductor behaves like a wire, i.e. a short circuit5Energy stored• Resistors dissipate energy. They transform power intoheat, light, etc. and radiate it• Inductors STORE energy in the form of a magnetic field.Eventually, they return that energy to the circuit.– So, during some periods they absorb energy (have positivev and I according to passive sign convention), and duringothers they return that energy (have positive v and Iaccording to active sign convention)• The instantaneous power absorbed is the same as forall passive elements: p(t)=v(t)i(t)• In order to find the total energy that has been stored inthe inductor, we need to integrate this powerabsorbed:6Example7891011Voltage/Current division• Inductors in series– Same current through all of them– Voltage splits proportionally to their inductances (hence,voltage division formula applies)• Inductors in parallel– Same voltage in all of them– Absolute currents are, in general, unrelated. Changes incurrent are INVERSELY proportional to their
View Full Document