lecture14 - 14 Lecture 14 14.1 AC circuits capacitors and...

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14. Lecture 14 14.1 AC circuits: capacitors and inductors 14.1.1 Capacitors Consider a circuit as in fig.78 which is called a low-pass filter for reasons we will see shortly. The AC generator determines the potential V a = V 0 sin ω t (14.1) and we want to understand the behavior of the potential V b at point ( b ). It is first convenient to see what happens if, instead of a sine we have a square wave as in fig.79. This is equivalent to putting a battery which periodically switches polarities as we see in the same figure. When the battery is of one polarity it charges the capacitor in time τ = RC as we saw before. After the capacitor charges nothing else happens and V b remains equal to V 0 . When the battery switches polarity the capacitor first discharges and then it charges with the opposite sign so V b = V 0 and V b continues to be V 0 until the battery switches back again. We see that, except for a small delay of τ = RC the potential V b follows the value at V a . In that sense the capacitor, for time scales t RC behaves as an open circuit. This last point should be emphasized, we assumed that the period with which we switched the battery was much larger than τ = RC . If we switch the battery very fast then the capacitor has no time to charge and discharge and the potential across it is zero. Namely V b = 0 and the capacitor is like a short-circuit, namely a cable.
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