RC Circuits UTD physics Spring 2024 As time approaches any point B, the voltage across the capacitor decays. However, it does not look as if the voltage has 'fully' decayed by the time that the voltage from the signal generator changes at point 5. (The fact that the slope of the capacitor voltage is not zero suggests this.) Remember that this voltage decay is asymptotic so that the slope would decrease a little more if the capacitor was left undisturbed. Similarly, it does not look as if the capacitor has 'fully' charged at any time marked '4' but the signal generator disturbs it before the slope gets near zero. Both the charging and the discharging of the capacitor are asymptotic and will not happen in any finite time. But if we don't disturb the capacitor (by letting the signal generator change voltage), both the charging & discharging will be visibly more complete. In the previous diagram, half the period of the generator (during which a single voltage decay occurs) is about 4t so the period of square waves from the signal generatoris T ~ 87. We'd get a better idea of the voltage being asymptotically approached if we used square waves of a longer period. How long? We want the voltage across Av(e) -t avio) the capacitor to be 'small' enough. Recall 16. What is the ratio of the voltage at t = 20t to the initial voltage across the capacitor? e 1 . . The implication is that we should use a low frequency such as fi,,, = Zor &t which to measure time constants. The circuit that you'll build in the lab is; Circuit 1 R=100kQ C=0.02uF At any moment, there is a difference between the voltage across the signal generator (square wave) and the voltage across the capacitor (exponential increase and decrease). In Electricity V we concluded that \"The sum of pressure differences around a loop that joins one end of the battery to the other is a constant that is a characteristic of the battery\" [This is part of statement 3 c in the model of electricity.] We spoke about pressure differences then, but subsequently replaced this with pofential differences or voltages. Statement 3 c refers to a battery because that was the source of voltage in Electricity V. The signal generator now plays the role of the battery in circuit 1. Statement 3 c tells us that the sum of voltages in circuit 1 is a constant (that is characteristic of the signal generator). In the context of circuit 1, the sum of voltages (that is being supplied by the signal generator) can't change between points A and B [where the sum is zero] or between B and A [where the sum is Vo # 0]. RC Circuits UTD physics Spring 2024 T e [ e ] > Vo Voltage (V) A B A B A B A time () At times slightly before A, the sum of voltages will be V;, [since square wave supplied by the signal generator is V,]. On the other hand, the graph of the capacitor voltage shows that V- is V,, slightly before moment A. However, if we choose a moment after A (for example, the moment half way between A and B), I/ is less than V. 17. How can the sum of voltages be a constant when V