Lecture 171• First order circuitsCharging 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).2Step function3Discharging of an inductor• An inductor is charged with a current k at time t=t0and we want to study how it discharges through a resistor4Discharging of a capacitor5General 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 inductor6Example7Example (cont)8Example 29Example
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