ECE 201 Lecture 18 Borja Peleato First order circuits with step inputs 1 Review In the last lecture we saw an expression for the discharging of a capacitor or inductor through a resistor The time it took Vc or IL to decrease by a factor of e was given by the time constant Even if the capacitor inductor is not directly connected to a resistor we can find how fast it discharges by computing the equivalent resistance of the rest of the circuit Today we extend that expression to cover charging AND discharging 2 Inductor charging Now lets see what happens while a capacitor or inductor charges 3 Capacitor charging 4 General case 5 Important remark The same formula can be applied to any voltage or current in a first order circuit You just need its initial and final values and the time constant of the L or C HOWEVER it is almost always easier to find first the voltage across the capacitor or the current across the inductor Then you can find the capacitor current or inductor voltage by derivating and multiplying by C or L and apply KVL KCL to find other quantities 6 Example It is possible to combine charging and discharging 7 8 9 10 11 12 13 Example 2 14 15
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