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| 184_notes:conservation_theorems [2018/05/15 17:43] – curdemma | 184_notes:conservation_theorems [2020/08/24 19:26] – dmcpadden |
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| Chapters 18 and 19 (and Chapters 2, 3, 6, 11, and 13) in Matter and Interactions (4th edition) | Chapters 18 and 19 (and Chapters 2, 3, 6, 11, and 13) in Matter and Interactions (4th edition) |
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| [[184_notes:symmetry|Next Page: Symmetry and Mathematical Tools]] | /*[[184_notes:symmetry|Next Page: Symmetry and Mathematical Tools]] |
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| [[184_notes:magnetic_field|Previous Page: The Magnetic Field]] | [[184_notes:magnetic_field|Previous Page: The Magnetic Field]]*/ |
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| ===== Conservation Theorems ===== | ===== Conservation Theorems ===== |
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| === Resistors in a circuit === | === Resistors in a circuit === |
| {{ 184_notes:week8_6.png?300}} | [{{ 184_notes:week8_6.png?300|Resistors in series}}] |
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| [[184_notes:r_series|Two resistors in series]] (end-to-end) must have the same current running through them, but they can use different amounts of electric potential to drive that current depending on their individual resistances. This leads to their combined, effective result on the current in a circuit increasing the resistance of the circuit, | [[184_notes:r_series|Two resistors in series]] (end-to-end) must have the same current running through them, but they can use different amounts of electric potential to drive that current depending on their individual resistances. This leads to their combined, effective result on the current in a circuit increasing the resistance of the circuit, |
| $$R_{eq} = R_1 + R_2$$ | $$R_{eq} = R_1 + R_2$$ |
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| {{184_notes:week8_9.png?400 }} | [{{184_notes:week8_9.png?400|Resistors in parallel }}] |
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| [[184_notes:r_parallel|Two resistors in parallel]] (connected off the same branch) must use the same electric potential (by the loop rule), but they can drive different currents as long as the sum of those currents is equal to the total before the branch splits. This leads to their combine effective result as reducing the overall resistance of the circuit, | [[184_notes:r_parallel|Two resistors in parallel]] (connected off the same branch) must use the same electric potential (by the loop rule), but they can drive different currents as long as the sum of those currents is equal to the total before the branch splits. This leads to their combine effective result as reducing the overall resistance of the circuit, |
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| === Capacitors in a circuit === | === Capacitors in a circuit === |
| {{ 184_notes:week8_12.png?300}} | [{{ 184_notes:week8_12.png?300|capacitors in series}}] |
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| [[184_notes:c_series|Two capacitors in series]] (end-to-end) must have the same amount of stored charge, otherwise a current would be driven until such time that they did. This means that each of them can store a different amount of energy per unit charge, which depends on their individual capacitance. The result is reducing the overall capacitance of the circuit, | [[184_notes:c_series|Two capacitors in series]] (end-to-end) must have the same amount of stored charge, otherwise a current would be driven until such time that they did. This means that each of them can store a different amount of energy per unit charge, which depends on their individual capacitance. The result is reducing the overall capacitance of the circuit, |
| $$\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$$ | $$\dfrac{1}{C_{eq}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$$ |
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| {{184_notes:week8_15.png?400 }} | [{{184_notes:week8_15.png?400|Capacitors in parallel }}] |
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| [[184_notes:c_parallel|Two capacitors in parallel]] (connected off the same branch) must use the same energy per unit charge (because of the loop rule), but they can store different amounts of charge depending on their individual capacitances. The result is increasing the overall capacitance of the circuit, | [[184_notes:c_parallel|Two capacitors in parallel]] (connected off the same branch) must use the same energy per unit charge (because of the loop rule), but they can store different amounts of charge depending on their individual capacitances. The result is increasing the overall capacitance of the circuit, |
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| $$C_{eq} = C_1 + C_2$$ | $$C_{eq} = C_1 + C_2$$ |