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| 184_notes:c_series [2020/08/23 20:23] – dmcpadden | 184_notes:c_series [2021/03/18 02:49] – [Node Rule and Charge in Series] bartonmo | ||
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| [{{ 184_notes: | [{{ 184_notes: | ||
| - | Consider what happens to the charge around a circuit with two capacitors in series. After the circuit is connected, electrons begin to move through the wires and collect on one plate. For every electron that gets stuck on the plate, it pushes another negative off the opposite plate. This electron continues moving down the wire (providing the electron current) until it becomes stuck on the first plate of the second capacitor. This in turn pushes an electron off the second plate of the capacitor, that continues to travel toward the battery. Because of this chain reaction, **//the charge on each of the capacitors in series must be the same//**. (This is similar to how current was the same for resistors in series.) | + | Consider what happens to the charge around a circuit with two capacitors in series. After the circuit is connected, electrons begin to move through the wires and collect on one plate. For every electron that gets stuck on the plate, it pushes another negative off the opposite plate. This electron continues moving down the wire (providing the electron current) until it becomes stuck on the first plate of the second capacitor. This in turn pushes an electron off the second plate of the capacitor, that continues to travel toward the battery. Because of this chain reaction, **the charge on each of the capacitors in series must be the same**. (This is similar to how current was the same for resistors in series.) |
| $$Q_1=Q_2$$ | $$Q_1=Q_2$$ | ||
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| $$|\Delta V_{bat}|=|\Delta V_{C1}|+|\Delta V_{C2}|$$ | $$|\Delta V_{bat}|=|\Delta V_{C1}|+|\Delta V_{C2}|$$ | ||
| - | So just like for resistors in series, **//the electric potentials add together for capacitors in series//**. Again, here we have make the // | + | So just like for resistors in series, **the electric potentials add together for capacitors in series**. Again, here we have make the // |
| ==== Equivalent Capacitance ==== | ==== Equivalent Capacitance ==== | ||
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| $$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$$ | $$\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}$$ | ||
| - | Thus, to combine capacitors in series, you take the inverse sum of the capacitors. This is important because **//the combination of capacitors in series will have a smaller capacitance than either of the individual capacitors//**. | + | Thus, to combine capacitors in series, you take the inverse sum of the capacitors. This is important because **the combination of capacitors in series will have a smaller capacitance than either of the individual capacitors**. |
| ==== Examples ==== | ==== Examples ==== | ||
| [[: | [[: | ||