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lecture7 - 7 Lecture 7 7.1 Capacitor charge and discharge...

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7. Lecture 7 7.1 Capacitor charge and discharge In the same way we can charge a capacitor through a resistor we can also discharge it. In the circuit of fig.35 we have a switch with two positions. In one position the capacitor charges through resistor R 1 and in the other it discharges through resistor R 2 . The characteristic times are given by t charge = R 1 C and t charge = R 2 C . Notice that these are properties of the circuit. The capacitor itself has no characteristic time associated with it, it depends on both the capacity C and the resistance R . A more practical circuit substitutes the switch by an integrated circuit that does the same job. At the end of this lecture I put a description of the circuit we used in class and how you can build it yourself if you are interested. R C + - V Δ Battery R 1 2 Figure 35: By flipping the switch we can charge and discharge the capacitor. The charac- teristic times are given by t charge = R 1 C and t charge = R 2 C . 7.2 DC circuits 7.2.1 Resistors in series and parallel More complicated circuits include many components. Let us see now what happens if you connect several resistors in series. In that case the current going through all of – 46 –
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them is the same. On the other hand the potential di ff erence across the system is the sum of the potential di ff erences across each resistors. For example if we look at fig. 36 we see that the potential di ff erence V = V a V d = ( V a V b ) + ( V b V c ) + ( V c V d ) = V 1 + V 2 + V 3 . (7.1) Using Ohm’s law we find V 1 = IR 1 , V 2 = IR 2 , V 3 = IR 3 , (7.2) from where we obtain V = IR 1 + IR 2 + IR 3 = I ( R 1 + R 2 + R 3 ) = IR (7.3) So the total resistance is R = R 1 + R 2 + R 3 a simple rule to remember!. Notice that I , the current is the same for all resistors since charge is conserved therefore the same amount of charge has to circulate per unit time in each point of the circuit. This is not true if the circuit branches as we see in fig.37 a connection known as parallel. In this case the potential di ff erence across all of resistors is the same as is easily seen if you remember that all points connected by a cable are at the same potential. The total current however is split between the three branches as: I = I 1 + I 2 + I 3 (7.4) Again, this is because charge is conserved so the total charge entering the circuit is distributed among the three resistors. Again using Ohm’s law we have I = V R 1 + V R
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