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184_notes:r_series [2018/06/26 13:23] – [Circuit Diagrams] curdemma | 184_notes:r_series [2019/01/04 03:03] – dmcpadden | ||
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===== Resistors in Series ===== | ===== Resistors in Series ===== | ||
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{{youtube> | {{youtube> | ||
==== Circuit Diagrams ==== | ==== Circuit Diagrams ==== | ||
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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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==== Node Rule and Current in Series ==== | ==== Node Rule and Current in Series ==== | ||
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When two circuit elements are in series this means that **//all of the current that goes into the first element also goes into the second element// | When two circuit elements are in series this means that **//all of the current that goes into the first element also goes into the second element// | ||
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==== Loop Rule and Voltage in Series ==== | ==== Loop Rule and Voltage in Series ==== | ||
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For resistors in series, we can also say something about the difference in electric potential across each circuit element. Using the [[184_notes: | For resistors in series, we can also say something about the difference in electric potential across each circuit element. Using the [[184_notes: | ||
- | {{ 184_notes: | ||
Oftentimes, the changes in potential in the wires are so small compared to those over the resistors, that we //__assume the changes in electric potential across the wires are negligible__// | Oftentimes, the changes in potential in the wires are so small compared to those over the resistors, that we //__assume the changes in electric potential across the wires are negligible__// | ||
$$+|\Delta V_{bat}|-|\Delta V_1|-|\Delta V_2| = 0$$ | $$+|\Delta V_{bat}|-|\Delta V_1|-|\Delta V_2| = 0$$ | ||
- | Another way of saying this would be that the energy per charge coming from the battery must be distributed across the two resistors. You can see this in the graph above. | + | Another way of saying this would be that the energy per charge coming from the battery must be distributed across the two resistors. You can see this in the graph below. |
$$|\Delta V_{bat}|=|\Delta V_1| + |\Delta V_2|$$ | $$|\Delta V_{bat}|=|\Delta V_1| + |\Delta V_2|$$ | ||
This means that **//in a series circuit, the electric potentials add together// | This means that **//in a series circuit, the electric potentials add together// | ||
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+ | {{ 184_notes: | ||
- | {{ 184_notes:Week8_5b.png?200}} | + | {{ 184_notes:Week8_5a.png?200|Example: loop 2}} |
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- | {{ 184_notes:Week8_5a.png? | + | |
An easy trick to help with the loop rules is to mark which side of the circuit element (be it a battery, resistor, or capacitor) would have the higher electric potential with a (+) and which side would have the lower electric potential with a (-). When moving around the loop, if you go from a low potential to a high potential the $\Delta V$ will be positive. If you move from a high potential to a low potential the $\Delta V$ will be negative. For example, in our loop, we moved from the negative side of the battery to the positive side of the battery so we had a $+\Delta V_{bat}$ and we moved from the positive side of the resistors to the negative so we had a $-\Delta V_1$ and $-\Delta V_2$. If we changed the direction of our loop to be counterclockwise instead, we would have gotten $+\Delta V_1$ and $+\Delta V_2$ and $-\Delta V_{bat}$. Both of these loops would have given you the same equation however. | An easy trick to help with the loop rules is to mark which side of the circuit element (be it a battery, resistor, or capacitor) would have the higher electric potential with a (+) and which side would have the lower electric potential with a (-). When moving around the loop, if you go from a low potential to a high potential the $\Delta V$ will be positive. If you move from a high potential to a low potential the $\Delta V$ will be negative. For example, in our loop, we moved from the negative side of the battery to the positive side of the battery so we had a $+\Delta V_{bat}$ and we moved from the positive side of the resistors to the negative so we had a $-\Delta V_1$ and $-\Delta V_2$. If we changed the direction of our loop to be counterclockwise instead, we would have gotten $+\Delta V_1$ and $+\Delta V_2$ and $-\Delta V_{bat}$. Both of these loops would have given you the same equation however. | ||
==== Equivalent Resistance ==== | ==== Equivalent Resistance ==== | ||
- | {{184_notes: | ||
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: | ||
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: | ||
$$\Delta V_{bat}=I_1R_1+I_2R_2$$ | $$\Delta V_{bat}=I_1R_1+I_2R_2$$ |