184_notes:r_series

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184_notes:r_series [2018/06/26 13:40] – [Equivalent Resistance] curdemma184_notes:r_series [2020/08/23 20:20] – dmcpadden
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 Sections 19.2 and 19.3 in Matter and Interactions (4th edition) Sections 19.2 and 19.3 in Matter and Interactions (4th edition)
  
-[[184_notes:r_parallel|Next Page: Resistors in Parallel]]+/*[[184_notes:r_parallel|Next Page: Resistors in Parallel]] 
 + 
 +[[184_notes:cap_in_cir|Previous Page: Capacitors in a Circuit]]*/
  
 ===== Resistors in Series ===== ===== Resistors in Series =====
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 {{youtube>_j6jrTWTK7E?large}} {{youtube>_j6jrTWTK7E?large}}
 ==== Circuit Diagrams ==== ==== Circuit Diagrams ====
-[{{  184_notes:Week8_1.png?200|Resistor representation in a circuit}}]+[{{  184_notes:Week8_1.png?200|Resistor representation in a circuit diagram}}]
  
 Circuit diagrams are a simplified way to represent a circuit. In a circuit diagram, each element is represented by some kind of symbol and the wires are represented by lines. These diagrams are not very good for showing what is happening to surface charges or the electric field, but they do help visualize a circuit particularly for combinations of circuit elements and some of the more macroscopic properties.  Circuit diagrams are a simplified way to represent a circuit. In a circuit diagram, each element is represented by some kind of symbol and the wires are represented by lines. These diagrams are not very good for showing what is happening to surface charges or the electric field, but they do help visualize a circuit particularly for combinations of circuit elements and some of the more macroscopic properties. 
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 ==== Loop Rule and Voltage in Series ==== ==== Loop Rule and Voltage in Series ====
-[{{  184_notes:Week8_3.png?300|Energy drops throughout the circuit}}]+[{{  184_notes:Week8_3.png?300|Potential differences (or voltage drops) throughout the circuit}}]
 For resistors in series, we can also say something about the difference in electric potential across each circuit element. Using the [[184_notes:r_energy|loop rule]], we know that the sum of all of the changes in electric potential around a complete loop must equal zero. Consider the same series circuit above with the battery and two resistors. If we think about the electric potential or energy per charge going around the circuit, we know that the highest electric potential will be on the positive side of the battery. As the current moves through the wire, there would be a small drop in electric potential along the wire (from the electron collisions with the nuclei), but a much larger change in potential would occur over the resistor. Then again, there would be another small drop over the next wire with a larger change over the second resistor, with a final small drop over the wire that connects back to the battery. If we move from the negative plate of the battery back to the positive plate, then there is now a large gain in electric potential (instead of a drop), and we have returned to where we started.   For resistors in series, we can also say something about the difference in electric potential across each circuit element. Using the [[184_notes:r_energy|loop rule]], we know that the sum of all of the changes in electric potential around a complete loop must equal zero. Consider the same series circuit above with the battery and two resistors. If we think about the electric potential or energy per charge going around the circuit, we know that the highest electric potential will be on the positive side of the battery. As the current moves through the wire, there would be a small drop in electric potential along the wire (from the electron collisions with the nuclei), but a much larger change in potential would occur over the resistor. Then again, there would be another small drop over the next wire with a larger change over the second resistor, with a final small drop over the wire that connects back to the battery. If we move from the negative plate of the battery back to the positive plate, then there is now a large gain in electric potential (instead of a drop), and we have returned to where we started.  
  
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 $$|\Delta V_{bat}|=|\Delta V_1| + |\Delta V_2|$$ $$|\Delta V_{bat}|=|\Delta V_1| + |\Delta V_2|$$
 This means that **//in a series circuit, the electric potentials add together//**. This means that **//in a series circuit, the electric potentials add together//**.
-[{{184_notes:Week8_4.png?600|Graph of voltage/energy drops throughout the circuit  }}]+[{{184_notes:Week8_4.png?600|Graph of electric potential throughout the circuit. Note that the change in potential along the wires is very small compared to the change in potential across a resistor.  }}]
 {{  184_notes:Week8_5b.png?200|Example: loop 1}} {{  184_notes:Week8_5b.png?200|Example: loop 1}}
  
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 To simplify series circuits, we will often try to replace the series resistors with a single resistor that has the equivalent resistance as the combination of resistors. This would mean that you get to deal with one resistor instead of two for example. We can do this by comparing the circuit with two resistors to the circuit with the equivalent resistance. In both of these circuits we would want to keep the battery the same (would have the same $\Delta V_{bat}$) and keep the current coming out of the battery as the same (same $I_{bat}$). From the loop rule around the combination circuit, we know that: To simplify series circuits, we will often try to replace the series resistors with a single resistor that has the equivalent resistance as the combination of resistors. This would mean that you get to deal with one resistor instead of two for example. We can do this by comparing the circuit with two resistors to the circuit with the equivalent resistance. In both of these circuits we would want to keep the battery the same (would have the same $\Delta V_{bat}$) and keep the current coming out of the battery as the same (same $I_{bat}$). From the loop rule around the combination circuit, we know that:
 $$|\Delta V_{bat}|=|\Delta V_1| + |\Delta V_2|$$ $$|\Delta V_{bat}|=|\Delta V_1| + |\Delta V_2|$$
-[{{184_notes:Week8_6.png?400|Circuit with two resistors, $R V_1$ and $R V_2$, and its equivalent circuit with $R V_eq$  }}]+[{{184_notes:Week8_6.png?400|Circuit with two resistors, $R_1$ and $R_2$, and its equivalent circuit with $R_e$  }}]
 If we //__assume that our resistors are ohmic__//, then we can rewrite the potential changes in terms of the resistance and current: If we //__assume that our resistors are ohmic__//, then we can rewrite the potential changes in terms of the resistance and current:
 $$\Delta V_{bat}=I_1R_1+I_2R_2$$ $$\Delta V_{bat}=I_1R_1+I_2R_2$$
  • 184_notes/r_series.txt
  • Last modified: 2021/06/28 23:17
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