Lecture 17 First order circuits 1 Charging and discharging We saw that for DC inductors behave like short circuits and capacitors behave like open circuits This is because inductors do not react to a constant current and capacitors do not react to a constant voltage The voltage in the first case and the current in the second are 0 However it takes some time to get them charged with current in the case of the inductor and with voltage in the case of the capacitor During the next few lectures we study what happens while capacitors and inductors are getting charged and discharged If there are no independent sources this lecture If there are sources with step response or switches If there are sources with sinusoidal response For now we focus on circuits where there is only ONE capacitor OR inductor first order circuits 2 Step function 3 Discharging of an inductor An inductor is charged with a current k at time t t0 and we want to study how it discharges through a resistor 4 Discharging of a capacitor 5 General case A capacitor inductor is storing some energy in the form of a voltage current at time t0 This energy is going to be dissipated by a resistor The equations tell us that the voltage current in the capacitor inductor decreases from k to 0 exponentially The time constant of this exponential tells us how fast it decreases After seconds the value will have decreased by a factor of e After 2 seconds it will have decreased by e2 etc In general the equation is where x t can be the voltage in a capacitor or the current in an inductor 6 Example 7 Example cont 8 Example 2 9 Example cont 10
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