ECE 201 Lecture 14 Borja Peleato Inductance and Inductors 1 Inductance In practice cables have a tiny resistance so the voltage between both ends of a cable is not zero when a current is flowing through them V R I Apart from this voltage due to Ohm s law there is another component that we cannot explain with resistance only if the current is increasing the voltage seems to be larger than that predicted by Ohm s law If the current is decreasing the voltage seems to be smaller than that predicted by Ohm s law There is a voltage component which is proportional to the rate of variation of the current The proportionality factor is called inductance 2 Inductors If you arrange a very long cable into a coil it presents 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 The faster the current changes the bigger this voltage Inductor Ideal representation for a wire without resistance arranged into a coil Stores magnetic energy in the form of a magnetic field through the coil Represented by L Units Henry s H 3 Example Find the voltage induced in a 250mH inductor when the current changes by 50A every second 4 Integral relationship This means that I can find the current from the voltage but only up to a certain constant i t0 is called the initial condition If I want to know the exact current in an inductor I need to know the voltage and the initial condition Think of it as finding the speed of a car from its acceleration 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 ideal inductor behaves like a wire i e a short circuit 5 Energy stored Resistors dissipate energy They transform power into heat 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 positive v and I according to passive sign convention and during others they return that energy have positive v and I according to active sign convention The instantaneous power absorbed is the same as for all passive elements p t v t i t In order to find the total energy that has been stored in the inductor we need to integrate this power absorbed 6 Example 7 8 9 10 11 Voltage 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 in current are INVERSELY proportional to their inductances 12
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